<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls54 ws0">a) Re<span class="_0 blank"> </span><span class="v1">1</span></div><div class="t m0 x2 h3 y2 ff1 fs0 fc0 sc0 ls54 ws1">2 + <span class="ff2 ls0">\u0131</span><span class="ws0 v1">b) Im<span class="_1 blank"> </span></span><span class="v2">2 + <span class="ff2">\u0131</span></span></div><div class="t m0 x3 h4 y2 ff1 fs0 fc0 sc0 ls1 ws2">3+4<span class="_2 blank"></span><span class="ff2 ls2">\u0131<span class="ff1 ls54 ws3 v1">c) Re </span><span class="ls3 v1">z</span><span class="ff3 fs1 ls4 v3">3</span><span class="ff1 ls54 ws4 v1">d) Im </span><span class="ls3 v1">z</span><span class="ff3 fs1 ls5 v3">4</span><span class="ff1 ls54 ws0 v1">e) Re<span class="_3 blank"> </span><span class="ws1 v1">(1 + <span class="ff2 ws5">\u0131<span class="ff1 ws6">)<span class="ff3 fs1 v4">2</span></span></span></span></span></span></div><div class="t m0 x4 h5 y2 ff1 fs0 fc0 sc0 ls1 ws2">3+2<span class="_2 blank"></span><span class="ff2 ls54">\u0131</span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls54 ws7">f )<span class="_4 blank"> </span><span class="ff4 ws8">|<span class="ff2 ls3">z</span>|<span class="ff3 fs1 ls6 v5">2</span></span><span class="ws0">h) Im<span class="_5 blank"> </span><span class="v1">1</span></span></div><div class="t m0 x3 h6 y4 ff2 fs0 fc0 sc0 ls7">z<span class="ff3 fs1 ls8 v6">2</span><span class="ff1 ls54 ws9 v1">i) <span class="ff5 v7">\ue00c</span></span></div><div class="t m0 x5 h7 y5 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 x5 h7 y6 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 x5 h7 y7 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 x6 h5 y8 ff1 fs0 fc0 sc0 ls1 ws2">1+4<span class="_2 blank"></span><span class="ff2 ls54">\u0131</span></div><div class="t m0 x7 h6 y4 ff1 fs0 fc0 sc0 ls54 ws1">4 + <span class="ff2 ls9">\u0131</span><span class="ff5 v8">\ue00c</span></div><div class="t m0 x8 h7 y5 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 x8 h7 y6 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 x8 h7 y7 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 x9 h8 y3 ff1 fs0 fc0 sc0 ls54 wsa">j) <span class="ff5 v7">\ue00c</span></div><div class="t m0 xa h7 y5 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 xa h7 y6 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 xa h7 y7 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 xb h5 y8 ff2 fs0 fc0 sc0 lsa">z<span class="ff4 lsb">\u2212<span class="ff1 ls54">1</span></span></div><div class="t m0 xb h6 y4 ff2 fs0 fc0 sc0 lsa">z<span class="ff1 ls54 wsb">+<span class="_6 blank"> </span>1 <span class="ff5 v8">\ue00c</span></span></div><div class="t m0 xc h7 y5 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 xc h7 y6 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 xc h7 y7 ff5 fs0 fc0 sc0 ls54">\ue00c</div><div class="t m0 xd h5 y3 ff1 fs0 fc0 sc0 ls54 ws6">k)<span class="ff4 lsc">|</span><span class="wsc">cos <span class="ff2 lsd">\u03b8</span><span class="lse">+<span class="ff2 lsf">\u0131</span></span><span class="wsd">sen <span class="ff2 ls10">\u03b8</span><span class="ff4 ws8">|<span class="ff2">.</span></span></span></span></div><div class="t m0 xe h9 y9 ff2 fs0 fc0 sc0 ls11">z<span class="ff1 ls54 ws1">+ 3</span><span class="ls12">\u0131<span class="ff1 ls13">=</span></span>z<span class="ff4 lsb">\u2212<span class="ff1 ls54 ws6">3</span></span><span class="ls54 wse">\u0131<span class="_7 blank"> </span>\u0131z <span class="ff1 ls13">=<span class="ff4 ls14">\u2212</span></span><span class="wsf">\u0131z <span class="ff1 ws1 v1">(2 + </span><span class="ws5 v1">\u0131<span class="ff1 ws6">)<span class="ff3 fs1 v4">2</span></span></span></span></span></div><div class="t m0 xf ha ya ff1 fs0 fc0 sc0 ls15">3<span class="ff4 lsb">\u2212</span><span class="ls54 ws6">4<span class="ff2 ls16">\u0131</span><span class="ws0 v1">= 1<span class="_7 blank"> </span><span class="ff4 ws8">|</span></span><span class="v1">(2<span class="ff2 ls11">z</span><span class="ws1">+ 5)(<span class="ff4 ws8 v9">\u221a</span><span class="ls15">2<span class="ff4 lsb">\u2212</span></span><span class="ff2 ws5">\u0131</span></span>)<span class="ff4 ls17">|</span><span class="ls18">=</span><span class="ff4 ws8 v9">\u221a</span><span class="ls19">3</span><span class="ff4 ws8">|</span>2<span class="ff2 lsa">z</span><span class="ws1">+ 5<span class="ff4">|</span></span></span></span></div><div class="t m0 x10 h5 yb ff1 fs0 fc0 sc0 ls54 ws10">arg(<span class="ff2 ls3">z</span>)</div><div class="t m0 xe h2 yc ff2 fs0 fc0 sc0 ls1a">z<span class="ff1 ls1b">=</span><span class="ls54 ws5 v1">z<span class="ff3 fs1 va">1</span></span></div><div class="t m0 x11 h5 yd ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 va">2</span></div><div class="t m0 x12 hb yc ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 ls1c va">2</span><span class="ff4 ws8">6<span class="ff1 ws0">= 0<span class="_8 blank"> </span></span></span><span class="ls1a">z<span class="ff1 ls13">=</span><span class="ls3">z</span></span><span class="ff6 fs1 v5">n</span></div><div class="t m0 x13 hc ye ff3 fs1 fc0 sc0 ls1d">1<span class="ff2 fs0 ls1e vb">n<span class="ff1 ls54 ws0">= 1<span class="ff2 ls1f">,</span><span class="ws6">2<span class="ff2 ws11">, . . .<span class="_9 blank"> </span>z<span class="_a blank"> </span></span><span class="ls20">=</span><span class="ff4 ws8 v1">\u2212</span><span class="v1">2</span></span></span></span></div><div class="t m0 x14 hd yf ff1 fs0 fc0 sc0 ls54 ws1">1 + <span class="ff2 ws5">\u0131<span class="ff4 ls21 vc">\u221a</span></span><span class="ls22">3<span class="ff2 ls23 vd">z</span><span class="ls24 vd">=</span></span><span class="ff2 ve">\u0131</span></div><div class="t m0 x15 ha yd ff4 fs0 fc0 sc0 ls14">\u2212<span class="ff1 ls25">2</span><span class="lsb">\u2212<span class="ff1 ls54 ws6">2<span class="ff2 ls26">\u0131<span class="ls23 v1">z</span></span><span class="ws0 v1">= (</span></span><span class="ls21 vf">\u221a</span><span class="ff1 ls15 v1">3</span><span class="v1">\u2212<span class="ff2 ls54 ws5">\u0131<span class="ff1 ws6">)<span class="ff3 fs1 v5">6</span></span></span></span></span></div><div class="t m0 xe he y10 ff2 fs0 fc0 sc0 ls54 ws5">\u0131<span class="ff1 ws12">(1 <span class="ff4 ls27">\u2212</span></span>\u0131<span class="ff4 ws8 v9">\u221a</span><span class="ff1 ws6">3)(<span class="ff4 ws8 v9">\u221a</span><span class="ws1">3 + </span></span>\u0131<span class="ff1 ws1">)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>2 + 2<span class="ff4 ls21 v9">\u221a</span><span class="ws6">3</span></span><span class="ls28">\u0131</span><span class="ff1 ws6">(<span class="ff4 ls14">\u2212</span><span class="ws1">1 + </span></span>\u0131<span class="ff1 ws6">)<span class="ff3 fs1 ls1c v5">7</span><span class="ls18">=</span><span class="ff4 ws8">\u2212</span><span class="ws1">8(1 + </span></span>\u0131<span class="ff1 ws1">)<span class="_b blank"> </span>(1 + </span>\u0131<span class="ff4 ls21 v9">\u221a</span><span class="ff1 ws6">3)<span class="ff7 fs1 ws13 v5">\u2212<span class="ff3 ws14">10 </span></span><span class="ws0">= 2<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls54 ws15">11 </span></span><span class="ls2a">(</span><span class="ff4 ws8">\u2212</span><span class="ws1">1 + </span></span></span>\u0131<span class="ff4 ls21 v9">\u221a</span><span class="ff1 ws6">3)</span>.</div><div class="t m0 x16 h5 y11 ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 ls2b va">0</span><span class="ws16">R z</span></div><div class="t m0 x17 h5 y12 ff2 fs0 fc0 sc0 ls2c">R<span class="ff4 ls54 ws8">\u2212</span><span class="ls54 ws5">z<span class="ff3 fs1 ls2d va">0</span>z</span></div><div class="t m0 xe hf y13 ff4 fs0 fc0 sc0 ls54 ws8">|<span class="ff2 ls11">z<span class="ff1 ls2e">+</span><span class="ls54 ws5">z<span class="ff3 fs1 ls2f va">0</span></span></span><span class="ls17">|<span class="ff1 ls13">=</span></span><span class="ff2 ws17">R<span class="_c blank"> </span>z <span class="ff1 lse">+</span><span class="ws5">z<span class="ff3 fs1 ls1c va">0</span><span class="ff1 ls13">=</span><span class="ls30">R</span></span></span>{<span class="ff1 ws6">cos(<span class="ff2 ws5">\u03c6</span><span class="ws1">) + <span class="ff2 ls31">\u0131</span></span>sen(<span class="ff2 ws5">\u03c6</span><span class="ls2a">)</span></span><span class="ls32">}<span class="ff2 ls33">\u03c6</span><span class="ls34">\u2208<span class="ff8 ls35">R</span></span></span><span class="ff2 ws18">z z<span class="_4 blank"> </span><span class="ff1 ls2e">+</span><span class="ls3">z<span class="ff3 fs1 ls2f va">0</span><span class="ls11">z<span class="ff1 ls2e">+</span></span></span><span class="ws5">z<span class="ff3 fs1 ls2f va">0</span><span class="lsa">z<span class="ff1 lse">+</span></span>z<span class="ff3 fs1 ls2f va">0</span><span class="ls7">z<span class="ff3 fs1 ls36 va">0</span><span class="ff1 ls13">=</span><span class="ls30">R</span></span><span class="ff3 fs1 v5">2</span></span></span></div><div class="t m0 x18 h10 y14 ff2 fs0 fc0 sc0 ls54 ws19">z<span class="_d blank"> </span>z <span class="ff1 ls18">=</span><span class="ws18">z<span class="_e blank"> </span>z<span class="_f blank"> </span>z <span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ws0">= (</span><span class="ls3">z</span><span class="ff1 ws6">)<span class="ff3 fs1 v5">2</span></span></span></div><div class="t m0 x19 h5 y15 ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 ls2f va">1</span>z<span class="ff3 fs1 ls37 va">2</span><span class="ff4 ws8">6<span class="ff1 ws1a">= 0<span class="_10 blank"> </span>Re(</span></span>z<span class="ff3 fs1 ls2f va">1</span><span class="ls3">z<span class="ff3 fs1 ls2f va">2</span></span><span class="ff1 ws1b">) = <span class="ff4 ws8">|</span></span>z<span class="ff3 fs1 ls38 va">1</span><span class="ff4 ws8">||</span>z<span class="ff3 fs1 ls38 va">2</span><span class="ff4">|</span></div><div class="t m0 x1a h5 y16 ff1 fs0 fc0 sc0 ls54 ws1c">arg(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">2</span></span><span class="ws10">)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>arg (<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="ls39">)<span class="ff4 lsb">±</span></span><span class="ws6">2<span class="ff2 ws1d">n\u03c0<span class="_11 blank"> </span>n </span><span class="ws0">= 0<span class="ff2 ls1f">,</span></span>1<span class="ff2 ls3a">,</span>2<span class="ff2 ws11">, . . .</span></span></span></div><div class="t m0 x1b h5 y17 ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 ls2f va">1</span>z<span class="ff3 fs1 ls3b va">2</span><span class="ff4 ws8">6<span class="ff1 ws1e">= 0<span class="_12 blank"> </span></span>|</span>z<span class="ff3 fs1 ls3c va">1</span><span class="ff1 ls3d">+</span>z<span class="ff3 fs1 ls2f va">2</span><span class="ff4 ls3e">|<span class="ff1 ls3f">=</span><span class="ls54 ws8">|</span></span>z<span class="ff3 fs1 ls38 va">1</span><span class="ff4 ls40">|<span class="ff1 ls41">+</span><span class="ls54 ws8">|</span></span>z<span class="ff3 fs1 ls38 va">2</span><span class="ff4">|</span></div><div class="t m0 x1a h5 y18 ff1 fs0 fc0 sc0 ls54 ws10">arg(<span class="ff2 ws5">z<span class="ff3 fs1 ls38 va">2</span></span>)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>arg (<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="ls39">)<span class="ff4 lsb">±</span></span><span class="ws6">2<span class="ff2 ws1d">n\u03c0<span class="_11 blank"> </span>n </span><span class="ws0">= 0<span class="ff2 ls1f">,</span></span>1<span class="ff2 ls1f">,</span>2<span class="ff2 ws11">, . . .</span></span></div><div class="t m0 x16 h5 y19 ff2 fs0 fc0 sc0 ls42">n<span class="ff4 ls43">\u2265<span class="ff1 ls44">1</span></span><span class="ls23">z<span class="ff4 ls54 ws8">6<span class="ff1 ws0">= 1</span></span></span></div><div class="t m0 x1c h11 y1a ff1 fs0 fc0 sc0 ls54 ws1">1 + <span class="ff2 lsa">z</span><span class="ls2e">+<span class="ff2 ls3">z<span class="ff3 fs1 ls45 v5">2</span></span>+</span><span class="ff4 ws1f">· · ·<span class="_6 blank"> </span></span><span class="ls2e">+<span class="ff2 ls3">z<span class="ff6 fs1 ls46 v5">n</span></span><span class="ls1b">=<span class="ls25 v1">1<span class="ff4 ls27">\u2212<span class="ff2 ls7">z</span></span></span></span></span><span class="ff6 fs1 ws20 v10">n<span class="ff3">+1</span></span></div><div class="t m0 x1d h5 y1b ff1 fs0 fc0 sc0 ls15">1<span class="ff4 lsb">\u2212<span class="ff2 ls54">z</span></span></div><div class="t m0 x1e h5 y1c ff1 fs0 fc0 sc0 ls47">0<span class="ff2 ls54 ws21">< \u03b8<span class="_a blank"> </span>< </span><span class="ls54 ws6">2<span class="ff2">\u03c0</span></span></div><div class="t m0 xe h12 y1d ff1 fs0 fc0 sc0 ls54 ws1">1 + cos(<span class="ff2 ls48">\u03b8</span>) + cos(2<span class="ff2 ls48">\u03b8</span>) + <span class="ff4 ws1f">· · ·<span class="_6 blank"> </span></span>+ cos(<span class="ff2 ws22">n\u03b8 </span><span class="ws0">) =<span class="_3 blank"> </span><span class="v1">1</span></span></div><div class="t m0 x1f h13 y1e ff1 fs0 fc0 sc0 ls49">2<span class="ls4a v1">+</span><span class="ls54 ws6 v11">sen[(<span class="ff2 ls4b">n<span class="ff1 ls4c">+<span class="ff3 fs1 ls54 v5">1</span></span></span></span></div><div class="t m0 x20 h14 y1f ff3 fs1 fc0 sc0 ls4d">2<span class="ff1 fs0 ls54 ws6 v4">)<span class="ff2 ls10">\u03b8</span>]</span></div><div class="t m0 x21 h5 y1e ff1 fs0 fc0 sc0 ls54 ws23">2 sen(<span class="ff2 ws24">\u03b8 /</span>2)</div><div class="t m0 x22 h2 y20 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls48">\u03b8</span><span class="ws1">) +<span class="_3 blank"> </span>sen(2<span class="ff2 ls48">\u03b8</span>) + <span class="ff4 ws1f">· · ·<span class="_6 blank"> </span></span><span class="ws25">+ sen(<span class="ff2 ws22">n\u03b8 </span><span class="ws0">) =<span class="_3 blank"> </span><span class="v1">1</span></span></span></span></div><div class="t m0 x23 h15 y21 ff1 fs0 fc0 sc0 ls4e">2<span class="ls54 ws6 v1">cot(<span class="ff2 ws24">\u03b8 /<span class="ff1 ws12">2) <span class="ff4 ls4f">\u2212</span></span></span><span class="v12">cos[(<span class="ff2 ls4b">n<span class="ff1 ls50">+<span class="ff3 fs1 ls54 v5">1</span></span></span></span></span></div><div class="t m0 x9 h16 y22 ff3 fs1 fc0 sc0 ls51">2<span class="ff1 fs0 ls2a v4">)<span class="ff2 ls48">\u03b8<span class="ff1 ls54">]</span></span></span></div><div class="t m0 x24 h5 y21 ff1 fs0 fc0 sc0 ls54 ws23">2 sen(<span class="ff2 ws24">\u03b8 /</span>2)</div><div class="t m0 x25 h5 y23 ff2 fs0 fc0 sc0 ls1a">z<span class="ff1 ls54 ws0">= cos(</span><span class="ls10">\u03b8<span class="ff1 ls54 ws26">) + </span><span class="ls31">\u0131<span class="ff1 ls54 ws6">sen(</span></span>\u03b8<span class="ff1 ls54">)</span></span></div><div class="t m0 x1a h2 y24 ff1 fs0 fc0 sc0 ls54 ws27">1 + cos(<span class="ff2 ls48">\u03b8</span><span class="ws28">) + <span class="ff2 ls31">\u0131</span><span class="ws6">sen(<span class="ff2 ls10">\u03b8</span></span></span>) + cos(2<span class="ff2 ls10">\u03b8</span><span class="ws29">) + <span class="ff2 ls31">\u0131</span><span class="ws6">sen(2<span class="ff2 ls48">\u03b8</span><span class="ws28">) + <span class="ff4 ws2a">· ·<span class="_13 blank"> </span>· </span><span class="ws2b">+ cos(<span class="ff2 ws22">n\u03b8 </span></span>) + <span class="ff2 ls52">\u0131</span></span>sen(<span class="ff2 ws22">n\u03b8 </span><span class="ws0">) =<span class="_3 blank"> </span><span class="ls25 v1">1<span class="ff4 ls27">\u2212</span></span></span><span class="v1">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls10">\u03b8</span><span class="ls53">]<span class="ff4 lsb">\u2212<span class="ff2 ls31">\u0131</span></span></span></span>sen[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span>]</span></span></span></span></div><div class="t m0 x26 h5 y25 ff1 fs0 fc0 sc0 ls25">1<span class="ff4 lsb">\u2212</span><span class="ls54 ws6">cos(<span class="ff2 ls48">\u03b8</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls31">\u0131</span></span></span>sen(<span class="ff2 ls10">\u03b8</span>)</span></div><div class="t m0 x27 h5 y26 ff1 fs0 fc0 sc0 ls54">\u2126</div><div class="t m0 x28 h2 y27 ff1 fs0 fc0 sc0 ls54 ws0">\u2126 =<span class="_3 blank"> </span><span class="ls15 v1">1<span class="ff4 lsb">\u2212</span></span><span class="ws6 v1">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ls4b">]<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span></span>sen[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls10">\u03b8</span>]</span></span></div><div class="t m0 x29 h5 y28 ff1 fs0 fc0 sc0 ls15">1<span class="ff4 lsb">\u2212</span><span class="ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span>sen(<span class="ff2 ls48">\u03b8</span>)</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x2a y0 w2 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg2.png"><div class="t m0 x11 h5 y29 ff1 fs0 fc0 sc0 ls54 ws2d">1 + cos(<span class="ff2 ls48">\u03b8</span>) + cos(2<span class="ff2 ls10">\u03b8</span><span class="ws2e">) + <span class="ff4 ws1f">· · ·<span class="_13 blank"> </span></span><span class="ws2f">+ cos(<span class="ff2 ws22">n\u03b8 </span><span class="ws30">)<span class="_14 blank"> </span>\u2126 sen(<span class="ff2 ls10">\u03b8</span></span>) +<span class="_3 blank"> </span>sen(2<span class="ff2 ls10">\u03b8</span></span>) + <span class="ff4 ws1f">· · · </span><span class="ws31">+ sen(<span class="ff2 ws22">n\u03b8 </span>)</span></span></div><div class="t m0 x2b h5 y2a ff1 fs0 fc0 sc0 ls54 ws32">\u2126 \u2126</div><div class="t m0 x25 h2 y2b ff1 fs0 fc0 sc0 ls54 ws0">\u2126 =<span class="_3 blank"> </span><span class="ls15 v1">1<span class="ff4 lsb">\u2212</span></span><span class="ws6 v1">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ls4b">]<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span></span>sen[(<span class="ff2 ls4b">n</span><span class="ws1">+ 1)<span class="ff2 ls10">\u03b8</span>]</span></span></div><div class="t m0 x2c h5 y2c ff1 fs0 fc0 sc0 ls15">1<span class="ff4 lsb">\u2212</span><span class="ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span>sen(<span class="ff2 ls48">\u03b8</span>)</span></div><div class="t m0 x2d h12 y2d ff1 fs0 fc0 sc0 ls1b">=<span class="ff4 ls55 v1">{</span><span class="ls25 v1">1<span class="ff4 ls27">\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ls53">]</span></span></span><span class="lsb">\u2212<span class="ff2 ls31">\u0131<span class="ff1 ls54 ws6">sen[(</span><span class="ls53">n<span class="ff1 ls54 ws1">+ 1)</span><span class="ls48">\u03b8<span class="ff1 ls56">]</span></span></span></span><span class="ls54 ws8">}{<span class="ff1 ls15">1</span></span>\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ws1">) + <span class="ff2 ls52">\u0131</span></span>sen(<span class="ff2 ls48">\u03b8</span><span class="ls2a">)</span><span class="ff4">}</span></span></span></span></span></div><div class="t m0 x2c h5 y2e ff4 fs0 fc0 sc0 ls55">{<span class="ff1 ls25">1</span><span class="ls27">\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls48">\u03b8</span><span class="ls39">)</span></span><span class="lsb">\u2212<span class="ff2 ls31">\u0131<span class="ff1 ls54 ws6">sen(</span><span class="ls10">\u03b8<span class="ff1 ls54 ws6">)</span></span></span><span class="ls54 ws8">}{<span class="ff1 ls15">1</span></span>\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ws1">) + <span class="ff2 ls31">\u0131</span></span>sen(<span class="ff2 ls10">\u03b8</span>)<span class="ff4">}</span></span></span></span></div><div class="t m0 x2d h2 y2f ff1 fs0 fc0 sc0 ls1b">=<span class="ff4 ls55 v1">{</span><span class="ls25 v1">1<span class="ff4 ls27">\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ls53">]</span></span></span><span class="lsb">\u2212<span class="ff2 ls31">\u0131<span class="ff1 ls54 ws6">sen[(</span><span class="ls53">n<span class="ff1 ls54 ws1">+ 1)</span><span class="ls48">\u03b8<span class="ff1 ls56">]</span></span></span></span><span class="ls54 ws8">}{<span class="ff1 ls15">1</span></span>\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ws1">) + <span class="ff2 ls52">\u0131</span></span>sen(<span class="ff2 ls48">\u03b8</span><span class="ls2a">)</span><span class="ff4">}</span></span></span></span></span></div><div class="t m0 x2e h18 y30 ff1 fs0 fc0 sc0 ls54 ws33">[1 <span class="ff4 lsb">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls38 v6">2</span></span>(<span class="ff2 ls48">\u03b8</span>)</span></div><div class="t m0 x2d h2 y31 ff1 fs0 fc0 sc0 ls1b">=<span class="ff4 ls55 v1">{</span><span class="ls25 v1">1<span class="ff4 ls27">\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ls56">]</span></span></span><span class="ls54 ws8">}{</span></span>1<span class="ff4 ls27">\u2212</span><span class="ls54 ws6">cos(<span class="ff2 ls48">\u03b8</span><span class="ls2a">)<span class="ff4 ls57">}</span></span><span class="ws25">+ sen[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ws23">] sen(<span class="ff2 ls48">\u03b8</span>)</span></span></span></span></span></div><div class="t m0 x2f h19 y32 ff1 fs0 fc0 sc0 ls54 ws33">[1 <span class="ff4 ls27">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls38 v6">2</span></span>(<span class="ff2 ls48">\u03b8</span>)</span></div><div class="t m0 x30 h2 y33 ff1 fs0 fc0 sc0 lse">+<span class="ff2 ls58">\u0131<span class="ff4 ls55 v1">{</span></span><span class="ls25 v1">1<span class="ff4 lsb">\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls4b">n</span><span class="ws1">+ 1)<span class="ff2 ls10">\u03b8</span></span>]</span><span class="ls59">}<span class="ff1 ls54 ws6">sen(<span class="ff2 ls48">\u03b8</span><span class="ls39">)</span></span><span class="ls5a">\u2212<span class="ff1 ls54 ws6">sen[(<span class="ff2 ls4b">n</span><span class="ws1">+ 1)<span class="ff2 ls10">\u03b8</span></span>]</span><span class="ls55">{<span class="ff1 ls15">1</span></span></span></span>\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls48">\u03b8</span><span class="ls2a">)</span><span class="ff4">}</span></span></span></span></div><div class="t m0 x31 h18 y34 ff1 fs0 fc0 sc0 ls54 ws33">[1 <span class="ff4 lsb">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls2f v6">2</span><span class="ls2a">(<span class="ff2 ls48">\u03b8</span></span>)</span></span></div><div class="t m0 x32 h5 y35 ff1 fs0 fc0 sc0 ls54 ws34">\u2126 = <span class="ff2 ls5b">\u03b1</span><span class="ls2e">+</span><span class="ff2">\u0131\u03b2</span></div><div class="t m0 x1b h2 y36 ff2 fs0 fc0 sc0 ls5c">\u03b1<span class="ff1 ls1b">=<span class="ff4 ls55 v1">{</span><span class="ls25 v1">1<span class="ff4 ls27">\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ls56">]</span></span></span><span class="ls54 ws8">}{</span></span>1<span class="ff4 ls27">\u2212</span><span class="ls54 ws6">cos(<span class="ff2 ls48">\u03b8</span><span class="ls2a">)<span class="ff4 ls57">}</span></span><span class="ws25">+ sen[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ws23">] sen(<span class="ff2 ls48">\u03b8</span>)</span></span></span></span></span></span></div><div class="t m0 x17 h18 y37 ff1 fs0 fc0 sc0 ls54 ws35">[1 <span class="ff4 lsb">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls38 v6">2</span></span>(<span class="ff2 ls48">\u03b8</span>)</span></div><div class="t m0 x33 h2 y38 ff1 fs0 fc0 sc0 ls1b">=<span class="ls15 v1">1<span class="ff4 lsb">\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ls39">)</span></span>\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span>] + cos[(<span class="ff2 ls53">n</span>+ 1)<span class="ff2 ls48">\u03b8</span><span class="ws23">] cos(<span class="ff2 ls10">\u03b8</span></span>) +<span class="_3 blank"> </span>sen[(<span class="ff2 ls53">n</span>+ 1)<span class="ff2 ls48">\u03b8</span><span class="ws23">] sen(<span class="ff2 ls48">\u03b8</span>)</span></span></span></span></span></div><div class="t m0 x2e h19 y39 ff1 fs0 fc0 sc0 ls54 ws33">[1 <span class="ff4 lsb">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls2f v6">2</span><span class="ls2a">(<span class="ff2 ls48">\u03b8</span></span>)</span></span></div><div class="t m0 x33 h2 y3a ff1 fs0 fc0 sc0 ls1b">=<span class="ls15 v1">1<span class="ff4 lsb">\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ls39">)</span></span>\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span>]) + cos[(<span class="ff2 ls53">n</span>+ 1)<span class="ff2 lsd">\u03b8</span></span></span>\u2212<span class="ff2 ls10">\u03b8<span class="ff1 ls54">]</span></span></span></span></div><div class="t m0 x34 h18 y3b ff1 fs0 fc0 sc0 ls54 ws33">[1 <span class="ff4 lsb">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls2f v6">2</span><span class="ls2a">(<span class="ff2 ls48">\u03b8</span></span>)</span></span></div><div class="t m0 x33 h2 y3c ff1 fs0 fc0 sc0 ls1b">=<span class="ls15 v1">1<span class="ff4 lsb">\u2212<span class="ff1 ls54 ws6">cos(<span class="ff2 ls10">\u03b8</span><span class="ls39">)</span></span>\u2212<span class="ff1 ls54 ws6">cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span>] + cos(<span class="ff2 ws22">n\u03b8 </span>)</span></span></span></span></div><div class="t m0 x35 h18 y3d ff1 fs0 fc0 sc0 ls54 ws33">[1 <span class="ff4 lsb">\u2212</span><span class="ws6">cos(<span class="ff2 ls10">\u03b8</span>)]<span class="ff3 fs1 ls45 v6">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls2f v6">2</span></span>(<span class="ff2 ls10">\u03b8</span>)</span></div><div class="t m0 x32 h1a y3e ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ls5d">A<span class="ff4 lsb">\u2212</span><span class="ls5e">B</span></span><span class="ls39">)<span class="ff4 lsb">\u2212</span></span>cos(<span class="ff2 ls5d">A</span><span class="ls2e">+<span class="ff2 ls5e">B</span></span><span class="ws0">) = 2<span class="_13 blank"> </span>sen(<span class="ff2 ws5">A</span><span class="ws23">) sen(<span class="_15 blank"></span><span class="ff2 ls5e">B<span class="ff1 ls54 ws36">)<span class="_16 blank"> </span>1 <span class="ff4 ls27">\u2212</span><span class="ws6">cos(</span></span><span class="ls5f">C<span class="ff1 ls54">)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>2 sen<span class="ff3 fs1 ls2f v5">2</span><span class="ls60">(</span><span class="ff6 fs1 v5">C</span></span></span></span></span></span></div><div class="t m0 x36 h14 y3f ff3 fs1 fc0 sc0 ls61">2<span class="ff1 fs0 ls54 v4">)</span></div><div class="t m0 x1b h1b y40 ff2 fs0 fc0 sc0 ls62">A<span class="ff1 ls54 ws0">= (</span><span class="ls53">n<span class="ff1 ls50">+<span class="ff3 fs1 ls54 v5">1</span></span></span></div><div class="t m0 x10 h16 y41 ff3 fs1 fc0 sc0 ls4d">2<span class="ff1 fs0 ls54 ws6 v4">)<span class="ff2 ws37">\u03b8<span class="_1 blank"> </span>B <span class="ff1 ls13">=</span><span class="ws24">\u03b8 /<span class="ff1 ls63">2</span><span class="ls64">C<span class="ff1 ls18">=</span></span>\u03b8</span></span></span></div><div class="t m0 x37 h1b y42 ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ws22">n\u03b8 </span><span class="ls39">)<span class="ff4 lsb">\u2212</span></span>cos[(<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ls48">\u03b8</span><span class="ws0">] = 2<span class="_13 blank"> </span>sen[(<span class="ff2 ls53">n</span><span class="ls50">+</span><span class="ff3 fs1 v5">1</span></span></span></div><div class="t m0 x38 h1c y43 ff3 fs1 fc0 sc0 ls4d">2<span class="ff1 fs0 ls54 ws6 v4">)<span class="ff2 ls48">\u03b8</span><span class="ws23">] sen(<span class="ff2 ws24">\u03b8 /</span><span class="ws38">2)<span class="_16 blank"> </span>1 <span class="ff4 lsb">\u2212</span></span></span>cos(<span class="ff2 ls10">\u03b8</span><span class="ws23">)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>2 sen</span></span><span class="ls38 v13">2</span><span class="ff1 fs0 ls54 ws6 v4">(<span class="ff2 ws24">\u03b8 /<span class="ff1">2)</span></span></span></div><div class="t m0 x39 h10 y44 ff1 fs0 fc0 sc0 ls54 ws12">(1 <span class="ff4 ls27">\u2212</span><span class="ws6">cos(<span class="ff2 ls48">\u03b8</span>))<span class="ff3 fs1 ls45 v5">2</span><span class="ws25">+ sen<span class="ff3 fs1 ls2f v5">2</span><span class="ls2a">(<span class="ff2 ls48">\u03b8</span></span><span class="ws39">)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>1 <span class="ff4 lsb">\u2212</span><span class="ws23">2 cos(<span class="ff2 ls10">\u03b8</span><span class="ws1">) + cos<span class="ff3 fs1 ls2f v5">2</span><span class="ls2a">(<span class="ff2 ls48">\u03b8</span></span>) +<span class="_3 blank"> </span>sen<span class="ff3 fs1 ls2f v5">2</span><span class="ls2a">(<span class="ff2 ls48">\u03b8</span></span><span class="ws3a">)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>2(1 <span class="ff4 lsb">\u2212</span></span></span></span></span></span>cos(<span class="ff2 ls48">\u03b8</span><span class="ws0">)) = 4<span class="_13 blank"> </span>sen<span class="ff3 fs1 ls38 v5">2</span></span>(<span class="ff2 ws24">\u03b8/</span>2)</span></div><div class="t m0 x33 h1d y45 ff2 fs0 fc0 sc0 ls65">\u03b1<span class="ff1 ls1b">=<span class="ls54 ws23 v12">2 sen</span><span class="ff3 fs1 ls38 v3">2</span><span class="ls54 ws6 v12">(</span></span><span class="ls54 ws24 v12">\u03b8 /<span class="ff1 ws1">2) + 2<span class="_13 blank"> </span>sen[(<span class="ff2 ls4b">n</span><span class="ls50">+</span><span class="ff3 fs1 v5">1</span></span></span></div><div class="t m0 x3a h14 y46 ff3 fs1 fc0 sc0 ls51">2<span class="ff1 fs0 ls2a v4">)<span class="ff2 ls48">\u03b8<span class="ff1 ls54 ws23">] sen(</span><span class="ls54 ws24">\u03b8 /<span class="ff1">2)</span></span></span></span></div><div class="t m0 x3b h13 y47 ff1 fs0 fc0 sc0 ls54 ws23">4 sen<span class="ff3 fs1 ls2f v6">2</span><span class="ws6">(<span class="ff2 ws24">\u03b8 /</span><span class="ws3b">2) <span class="ls66 v1">=</span></span><span class="v11">sen(<span class="ff2 ws24">\u03b8 /<span class="ff1 ws1">2) +<span class="_3 blank"> </span>sen[(</span><span class="ls4b">n<span class="ff1 ls4c">+</span></span><span class="ff3 fs1 v5">1</span></span></span></span></div><div class="t m0 x3c h14 y46 ff3 fs1 fc0 sc0 ls4d">2<span class="ff1 fs0 ls54 ws6 v4">)<span class="ff2 ls10">\u03b8</span>]</span></div><div class="t m0 x3d h5 y47 ff1 fs0 fc0 sc0 ls54 ws23">2 sen(<span class="ff2 ws24">\u03b8 /</span>2)</div><div class="t m0 x30 h5 y48 ff2 fs0 fc0 sc0 ls54 ws3c">\u03b2<span class="_3 blank"> </span>. . .</div><div class="t m0 xe h1e y49 ff1 fs0 fc0 sc0 ls54 ws6">(2<span class="ff2 ws5">\u0131</span>)<span class="ff3 fs1 ws3d v5">1<span class="ff6 ws20">/<span class="ff3 ls67">2</span></span></span><span class="ls2a">(</span><span class="ff4 ws8">\u2212<span class="ff2 ws5">\u0131</span></span>)<span class="ff3 fs1 ls68 v5">1<span class="ff6 ls54 ws20">/<span class="ff3 ls69">3</span></span></span><span class="ls2a">(</span><span class="ff4 ws8">\u2212</span>1)<span class="ff3 fs1 ws3d v5">1<span class="ff6 ws20">/<span class="ff3 ls67">3</span></span></span>8<span class="ff3 fs1 ws3d v5">1<span class="ff6 ws20">/<span class="ff3">6</span></span></span></div><div class="t m0 x3e h1f y4a ff1 fs0 fc0 sc0 ls2a">(<span class="ff4 ls54 ws8">\u2212</span><span class="ls54 ws1">1 + <span class="ff2 ws5">\u0131<span class="ff4 ls21 v9">\u221a</span></span><span class="ws6">3)<span class="ff3 fs1 ws3d v5">3<span class="ff6 ws20">/<span class="ff3 ls67">2</span></span></span></span></span>(<span class="ff4 ls54 ws8">\u2212</span><span class="ls54 ws6">1)<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls54 ws3d">3<span class="ff6 ws20">/</span>4</span></span></span></div><div class="t m0 x1c h10 y4b ff2 fs0 fc0 sc0 ls7">z<span class="ff3 fs1 ls6a v5">4</span><span class="ff1 ls54 ws3e">+ 4<span class="_3 blank"> </span>=<span class="_3 blank"> </span>0<span class="_17 blank"> </span></span>z<span class="ff3 fs1 ls6a v5">4</span><span class="ff1 ls54 ws3e">+ 4</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w2 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg3.png"><div class="t m0 x3f hb y29 ff2 fs0 fc0 sc0 ls6b">w<span class="ff4 ls54 ws8">6<span class="ff1 ws0">= 1<span class="_18 blank"> </span></span></span><span class="ls54 ws3f">n<span class="_19 blank"> </span>w <span class="ff6 fs1 ls46 v5">n</span><span class="ff1 ws0">= 1</span></span></div><div class="t m0 x40 hb y4c ff1 fs0 fc0 sc0 ls54 ws1">1 + <span class="ff2 ls6c">w</span><span class="ls2e">+<span class="ff2 ls6d">w<span class="ff3 fs1 ls45 v5">2</span></span>+</span><span class="ff4 ws1f">· · ·<span class="_6 blank"> </span></span><span class="lse">+<span class="ff2 ls6e">w</span></span><span class="ff6 fs1 ws20 v5">n<span class="ff7 ls29">\u2212<span class="ff3 ls1c">1</span></span></span><span class="ws0">= 0</span></div><div class="t m0 x29 h10 y4d ff2 fs0 fc0 sc0 ls54 ws40">az <span class="ff3 fs1 ls45 v5">2</span><span class="ff1 lse">+</span><span class="ws41">bz <span class="ff1 ls2e">+</span><span class="ls6f">c</span><span class="ff1 ws0">= 0<span class="_1a blank"> </span></span><span class="ws3c">a, b, c</span></span></div><div class="t m0 x41 h5 y4e ff2 fs0 fc0 sc0 ls70">a<span class="ff4 ls54 ws8">6<span class="ff1 ws0">= 0</span></span></div><div class="t m0 x32 h5 y4f ff2 fs0 fc0 sc0 ls54">a</div><div class="t m0 x31 h2 y50 ff2 fs0 fc0 sc0 ls3">z<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls71">+</span><span class="ls54 v1">b</span></div><div class="t m0 x7 h20 y51 ff2 fs0 fc0 sc0 ls72">a<span class="lsa v1">z<span class="ff1 ls73">+</span></span><span class="ls54 v2">c</span></div><div class="t m0 x24 h21 y51 ff2 fs0 fc0 sc0 ls74">a<span class="ff1 ls54 ws0 v1">= 0</span></div><div class="t m0 x42 h7 y52 ff5 fs0 fc0 sc0 ls54 ws42">\ue012<span class="ff2 ls11 v14">z<span class="ff1 ls75">+</span></span><span class="ff2 v15">b</span></div><div class="t m0 x2b h22 y53 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls72">a</span><span class="ff5 ws42 v16">\ue013</span><span class="ff3 fs1 v17">2</span></div><div class="t m0 x1c h23 y54 ff4 fs0 fc0 sc0 ls76">\u2212<span class="ff2 ls77 v1">b</span><span class="ff3 fs1 ls54 v10">2</span></div><div class="t m0 x43 h3 y53 ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a<span class="ff3 fs1 ls79 v6">2</span></span><span class="ls73 v1">+</span><span class="ff2 v2">c</span></div><div class="t m0 x44 h24 y53 ff2 fs0 fc0 sc0 ls7a">a<span class="ff1 ls54 ws0 v1">= 0<span class="_1b blank"> </span>=<span class="_1c blank"></span><span class="ff4 ls7b">\u21d2<span class="ff5 ls54 ws42 v11">\ue012</span><span class="ff2 lsa">z<span class="ff1 ls7c">+</span><span class="ls54 v1">b</span></span></span></span></div><div class="t m0 x45 h22 y53 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls7d">a</span><span class="ff5 ws42 v16">\ue013</span><span class="ff3 fs1 v17">2</span></div><div class="t m0 x46 h23 y54 ff1 fs0 fc0 sc0 ls1b">=<span class="ff2 ls7e v1">b</span><span class="ff3 fs1 ls45 v10">2</span><span class="ff4 lsb v1">\u2212</span><span class="ls54 ws6 v1">4<span class="ff2">ac</span></span></div><div class="t m0 x15 h18 y53 ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a</span><span class="ff3 fs1 v6">2</span></div><div class="t m0 x47 h10 y55 ff1 fs0 fc0 sc0 ls54 ws43">\u2206 = <span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span></span><span class="ws6">4<span class="ff2">ac</span></span></div><div class="t m0 x2e h7 y56 ff5 fs0 fc0 sc0 ls7f">\ue012<span class="ff2 lsa v14">z<span class="ff1 ls75">+<span class="ff2 ls54 v1">b</span></span></span></div><div class="t m0 x7 h22 y57 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls72">a<span class="ff5 ls7f v16">\ue013</span></span><span class="ff3 fs1 v17">2</span></div><div class="t m0 x48 h12 y58 ff1 fs0 fc0 sc0 ls80">=<span class="ls54 v1">\u2206</span></div><div class="t m0 x49 h18 y57 ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a</span><span class="ff3 fs1 v6">2</span></div><div class="t m0 x4a h12 y59 ff2 fs0 fc0 sc0 ls81">z<span class="ff1 ls82">+</span><span class="ls54 v1">b</span></div><div class="t m0 x4b h5 y5a ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2">a</span></div><div class="t m0 x4c h5 y5b ff1 fs0 fc0 sc0 ls54">\u2206</div><div class="t m0 x4d h18 y5a ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a</span><span class="ff3 fs1 v6">2</span></div><div class="t m0 x38 h7 y5c ff5 fs0 fc0 sc0 ls83">\ue012<span class="ff1 ls54 v15">\u2206</span></div><div class="t m0 x4e h25 y5d ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a<span class="ff3 fs1 ls84 v6">2</span></span><span class="ff5 ws42 v16">\ue013</span><span class="ff3 fs1 ws3d v17">1<span class="ff6 ls68">/</span>2</span></div><div class="t m0 x4b h2 y5e ff2 fs0 fc0 sc0 ls11">z<span class="ff1 ls75">+</span><span class="ls54 v1">b</span></div><div class="t m0 x4f h26 y5f ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls7a">a</span><span class="ls13 v1">=</span><span class="ff5 ls83 v16">\ue012</span><span class="v2">\u2206</span></div><div class="t m0 x23 h25 y5f ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a<span class="ff3 fs1 ls84 v6">2</span></span><span class="ff5 ws42 v16">\ue013</span><span class="ff3 fs1 ws3d v17">1<span class="ff6 ls68">/</span>2</span></div><div class="t m0 x4e h2 y5e ff1 fs0 fc0 sc0 ls54 ws6">=<span class="_1c blank"></span><span class="ff4 ls7b">\u21d2<span class="ff2 ls23">z<span class="ff1 ls13">=</span></span><span class="ls85">\u2212<span class="ff2 ls54 v1">b</span></span></span></div><div class="t m0 x50 h26 y5f ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls86">a</span><span class="ls2e v1">+</span><span class="ff5 ls87 v16">\ue012</span><span class="v2">\u2206</span></div><div class="t m0 x51 h25 y5f ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls78">a<span class="ff3 fs1 ls84 v6">2</span></span><span class="ff5 ws42 v16">\ue013</span><span class="ff3 fs1 ws3d v17">1<span class="ff6 ws20">/<span class="ff3">2</span></span></span></div><div class="t m0 x11 h5 y60 ff1 fs0 fc0 sc0 ls54 ws44">a) <span class="ff4 lsb">\u2212</span><span class="ff2 ws45">\u03c0<span class="_a blank"> </span>< </span><span class="ws10">arg(<span class="ff2 ls3">z</span><span class="ls88">)</span><span class="ff2 ws46"><<span class="_4 blank"> </span>\u03c0 ,<span class="_1d blank"> </span><span class="ff4 ws8">|</span><span class="ls7">z<span class="ff4 ls17">|</span><span class="ls13">></span></span></span><span class="ws47">2<span class="_1e blank"> </span>b) 1 <span class="ff2 ls18"><</span><span class="ff4 ws8">|<span class="ff2 lsa">z</span><span class="lsb">\u2212</span></span><span class="ws6">2<span class="ff2 ws5">\u0131<span class="ff4 ls17">|</span><span class="ls13"><</span></span><span class="ws48">2<span class="_1e blank"> </span>c) <span class="ff4 ws8">|</span></span>2<span class="ff2 lsa">z</span><span class="ws1">+ 3<span class="ff4 ls17">|<span class="ff2 ls18">></span></span>4</span></span></span></span></div><div class="t m0 x11 h10 y61 ff1 fs0 fc0 sc0 ls54 ws0">d) Im(<span class="ff2 ls3">z<span class="ff3 fs1 ls2f v5">2</span></span><span class="ls88">)<span class="ff2 ls18">></span></span>0<span class="_1f blank"> </span>e) Re(1<span class="ff2 ws49">/z </span><span class="ls88">)<span class="ff2 ls18"><</span></span><span class="ws6">1<span class="ff2 ws5">/</span><span class="ws7">2<span class="_20 blank"> </span>f )<span class="_4 blank"> </span><span class="ff4 ws8">|<span class="ff2 lsa">z</span><span class="lsb">\u2212</span></span></span>4<span class="ff4 ls17">|<span class="ff2 ls13">></span><span class="ls54 ws8">|<span class="ff2 ls3">z</span>|</span></span></span></div><div class="t m0 x11 h1f y62 ff1 fs0 fc0 sc0 ls54 ws0">g) Re(<span class="ff2 ls3">z<span class="ff3 fs1 ls2f v5">2</span></span><span class="ls88">)<span class="ff4 ls43">\u2265</span></span><span class="ws4a">1<span class="_21 blank"> </span>h) <span class="ff4 ws8">|</span><span class="ws10">arg(<span class="ff2 ls7">z</span><span class="ls2a">)<span class="ff4 ls89">|</span></span><span class="ff2 ws46"><<span class="_4 blank"> </span>\u03c0 /</span><span class="ws4b">4<span class="_20 blank"> </span>i) <span class="ff4 ws8">|</span><span class="ws6">(<span class="ff2 lsa">z<span class="ff4 ls27">\u2212</span><span class="ls54 ws5">\u0131</span></span><span class="ws4c">)(1 <span class="ff4 lsb">\u2212</span><span class="ff2 ws5">\u0131<span class="ff4 ls21 v9">\u221a</span></span></span>3)<span class="ff4 ls17">|</span></span></span></span></span>= 2<span class="ff4 ws8">|<span class="ff2 ls3">z</span>|</span></div><div class="t m0 x52 h10 y63 ff2 fs0 fc0 sc0 ls3">z<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls18">=</span><span class="ls8a">a<span class="ff1 lse">+</span><span class="ls54 ws19">b\u0131<span class="_22 blank"> </span>z <span class="ff1 ws0">= (</span><span class="ws4d">x,<span class="_13 blank"> </span>y<span class="ff1 ws4e">) = </span><span class="ls8b">x<span class="ff1 lse">+</span></span>\u0131y</span></span></span></div><div class="t m0 x32 h5 y64 ff2 fs0 fc0 sc0 ls1a">z<span class="ff1 ls13">=</span><span class="ls8c">x<span class="ff1 ls2e">+</span><span class="ls54">\u0131y</span></span></div><div class="t m0 x2c h10 y65 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 ls27">\u2212</span><span class="ls8e">y<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls54 ws1">+ 2</span><span class="ls54 ws46">xy \u0131<span class="_4 blank"> </span><span class="ff1 ws0">= (</span><span class="ls8c">x<span class="ff1 ls2e">+</span></span><span class="ws4f">\u0131y <span class="ff1 ls2a">)<span class="ff3 fs1 ls1c v5">2</span><span class="ls13">=</span></span><span class="ls3">z<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls18">=</span><span class="ls8a">a<span class="ff1 lse">+</span></span></span>\u0131b</span></span></span></div><div class="t m0 x53 hf y66 ff2 fs0 fc0 sc0 ls8f">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span><span class="ls8e">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls18">=</span><span class="ls90">a<span class="ff1 ls54 ws6">2</span><span class="ls54 ws50">xy <span class="ff1 ls13">=</span>b</span></span></span></div><div class="t m0 x47 h27 y67 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls13">=<span class="ff4 ls54 ws8">|</span></span><span class="ls3">z<span class="ff4 ls54 ws8">|<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls13">=</span>|</span>z<span class="ff4 ls54 ws8">||</span><span class="ls7">z<span class="ff4 ls17">|<span class="ff1 ls13">=</span><span class="ls54 ws8">|</span></span><span class="ls54 ws51">z z <span class="ff4 ls89">|<span class="ff1 ls18">=</span><span class="ls54 ws8">|</span></span></span>z<span class="ff3 fs1 ls38 v5">2</span><span class="ff4 ls89">|<span class="ff1 ls18">=</span><span class="ls54 ws8">|</span></span><span class="ls8a">a<span class="ff1 lse">+</span><span class="ls54 ws5">\u0131b<span class="ff4 ls89">|<span class="ff1 ls18">=</span><span class="ls21 v9">\u221a</span></span>a<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 lse">+</span><span class="ls7e">b</span><span class="ff3 fs1 v6">2</span></span></span></span></span></span></div><div class="t m0 x1f h28 y68 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls18">=<span class="ff4 ls54 ws8 v9">\u221a</span></span><span class="ls78">a<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls77">b<span class="ff3 fs1 ls54 v6">2</span></span></span></span></div><div class="t m0 x1f hf y69 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span><span class="ls91">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls18">=</span><span class="ls54">a</span></span></div><div class="t m0 x3a h5 y6a ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ws52">xy </span><span class="ls18">=</span><span class="ff2">b</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w3 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg4.png"><div class="t m0 x2b h27 y6b ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls8d">x<span class="ff3 fs1 ls36 v5">2</span></span><span class="ls13">=<span class="ff4 ls21 v9">\u221a</span><span class="ff2 ls78">a<span class="ff3 fs1 ls45 v6">2</span></span><span class="ls2e">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span></span>+<span class="ff2 ls92">a</span></span></span>2<span class="ff2 ls91">y<span class="ff3 fs1 ls1c v5">2</span></span><span class="ls18">=</span><span class="ff4 ws8 v9">\u221a</span><span class="ff2 ls78">a<span class="ff3 fs1 ls45 v6">2</span></span><span class="ls2e">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 ls27">\u2212</span><span class="ls54">a</span></span></span></div><div class="t m0 x54 h5 y6c ff4 fs0 fc0 sc0 ls21">\u221a<span class="ff2 ls78 v18">a</span><span class="ff3 fs1 ls45 v19">2</span><span class="ff1 ls2e v18">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls36 v6">2</span><span class="ff4 ls54 ws53">\u2265 |</span><span class="ls78">a<span class="ff4 ls54">|</span></span></span></span></div><div class="t m0 x12 h29 y6d ff2 fs0 fc0 sc0 ls78">a<span class="ff3 fs1 ls93 v5">2</span><span class="ff1 ls94">+</span><span class="ls7e">b<span class="ff3 fs1 ls95 v5">2</span><span class="ff4 ls96">\u2265</span></span>a<span class="ff3 fs1 ls97 v5">2</span><span class="ff4 ls21 v9">\u221a</span>a<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls7e">b<span class="ff3 fs1 ls98 v6">2</span><span class="ff4 ls96">\u2265<span class="ls21 v1a">\u221a</span></span></span>a<span class="ff3 fs1 ls95 v6">2</span><span class="ff1 ls99">=<span class="ff4 ls54 ws8">|</span></span>a<span class="ff4 ls54">|</span></div><div class="t m0 x55 h2a y6e ff2 fs0 fc0 sc0 ls9a">x<span class="ff1 ls13">=<span class="ff4 ls14">±<span class="ff5 ls9b v1b">s</span><span class="ls54 ws8 v1c">\u221a</span></span></span><span class="ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span><span class="ff1 ls2e v1">+</span><span class="ls77 v1">b</span><span class="ff3 fs1 ls45 v1d">2</span><span class="ff1 ls2e v1">+</span><span class="ls54 v1">a</span></div><div class="t m0 x56 h2b y6f ff1 fs0 fc0 sc0 ls9c">2<span class="ff2 ls9d v1">y</span><span class="ls13 v1">=<span class="ff4 ls14">±<span class="ff5 ls9e v1b">s</span><span class="ls21 v1c">\u221a</span><span class="ff2 ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span></span><span class="ls2e v2">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 ls27">\u2212</span><span class="ls54">a</span></span></span></div><div class="t m0 x3d h5 y6f ff1 fs0 fc0 sc0 ls54">2</div><div class="t m0 x57 h5 y70 ff2 fs0 fc0 sc0 ls54 ws54">x y<span class="_23 blank"> </span><span class="ff4">±</span></div><div class="t m0 x1a h5 y71 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ws50">xy </span><span class="ls13">=</span><span class="ff2 ws55">b<span class="_24 blank"> </span>b > </span><span class="ls9f">0</span><span class="ff2 ws56">x > </span><span class="ls63">0</span><span class="ff2 ws57">y<span class="_a blank"> </span>> </span><span class="lsa0">0</span><span class="ff2 ws58">x < </span><span class="lsa1">0</span><span class="ff2 ws57">y<span class="_a blank"> </span>< </span>0</div><div class="t m0 x58 h2a y72 ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 ls1c va">1</span><span class="ff1 ls18">=<span class="ff5 ls9b v1b">s</span></span><span class="ff4 ws8 v1c">\u221a</span><span class="ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span><span class="ff1 lse v1">+</span><span class="ls7e v1">b</span><span class="ff3 fs1 ls45 v1d">2</span><span class="ff1 ls2e v1">+</span><span class="v1">a</span></div><div class="t m0 x57 h2b y73 ff1 fs0 fc0 sc0 lsa2">2<span class="ls2e v1">+<span class="ff2 ls54 ws5">\u0131<span class="ff5 ls9b v1b">s</span><span class="ff4 ls21 v1c">\u221a</span><span class="ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span><span class="v1">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 lsb">\u2212</span><span class="ls54">a</span></span></span></span></div><div class="t m0 x56 h2b y73 ff1 fs0 fc0 sc0 lsa3">2<span class="ff2 ls54 ws59 v1">, z</span><span class="ff3 fs1 ls1c v1e">2</span><span class="ls18 v1">=<span class="ff4 ls54 ws8">\u2212<span class="ff5 ls9b v1b">s</span><span class="v1c">\u221a</span><span class="ff2 ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span></span><span class="lse v2">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls54">a</span></span></span></div><div class="t m0 x51 h2b y73 ff1 fs0 fc0 sc0 lsa2">2<span class="ff4 lsb v1">\u2212<span class="ff2 ls54 ws5">\u0131<span class="ff5 ls9b v1b">s</span><span class="ff4 ls21 v1c">\u221a</span><span class="ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span></span><span class="ls2e v2">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 lsb">\u2212</span><span class="ls54">a</span></span></span></div><div class="t m0 x59 h5 y73 ff1 fs0 fc0 sc0 ls54">2</div><div class="t m0 x5a h5 y74 ff2 fs0 fc0 sc0 ls54 ws5a">b < <span class="ff1 lsa4">0</span><span class="ws56">x > <span class="ff1 ls63">0</span><span class="ws57">y<span class="_a blank"> </span>< <span class="ff1 lsa0">0</span><span class="ws58">x < <span class="ff1 ls63">0</span><span class="ws5b">y<span class="_a blank"> </span>> <span class="ff1">0</span></span></span></span></span></div><div class="t m0 x58 h2a y75 ff2 fs0 fc0 sc0 ls54 ws5">z<span class="ff3 fs1 ls1c va">1</span><span class="ff1 ls18">=<span class="ff5 ls9b v1b">s</span></span><span class="ff4 ws8 v1c">\u221a</span><span class="ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span><span class="ff1 lse v1">+</span><span class="ls7e v1">b</span><span class="ff3 fs1 ls45 v1d">2</span><span class="ff1 ls2e v1">+</span><span class="v1">a</span></div><div class="t m0 x57 h2b y76 ff1 fs0 fc0 sc0 lsa2">2<span class="ff4 lsb v1">\u2212<span class="ff2 ls54 ws5">\u0131<span class="ff5 ls9b v1b">s</span><span class="ff4 ls21 v1c">\u221a</span><span class="v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span></span><span class="lse v2">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 lsb">\u2212</span><span class="ls54">a</span></span></span></div><div class="t m0 x1f h2b y76 ff1 fs0 fc0 sc0 lsa3">2<span class="ff2 ls54 ws59 v1">, z</span><span class="ff3 fs1 ls1c v1e">2</span><span class="ls13 v1">=<span class="ff4 ls14">\u2212<span class="ff5 ls9b v1b">s</span><span class="ls54 ws8 v1c">\u221a</span><span class="ff2 ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span></span><span class="ls2e v2">+<span class="ff2 ls77">b<span class="ff3 fs1 ls45 v6">2</span></span>+<span class="ff2 ls54">a</span></span></div><div class="t m0 x51 h2b y76 ff1 fs0 fc0 sc0 lsa2">2<span class="ls2e v1">+<span class="ff2 ls54 ws5">\u0131<span class="ff5 ls9b v1b">s</span><span class="ff4 ls21 v1c">\u221a</span><span class="ls78 v1">a</span><span class="ff3 fs1 ls45 v1d">2</span></span><span class="v1">+<span class="ff2 ls7e">b<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 lsb">\u2212</span><span class="ls54">a</span></span></span></span></div><div class="t m0 x59 h5 y76 ff1 fs0 fc0 sc0 ls54">2</div><div class="t m0 x5b h10 y77 ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 ls3">z<span class="ff3 fs1 ls45 v5">4</span><span class="ff4 lsb">\u2212</span></span>16)(<span class="ff2 ls3">z<span class="ff3 fs1 ls45 v5">3</span></span><span class="ws0">+<span class="_6 blank"> </span>1) = 0</span></div><div class="t m0 x5c h1e y78 ff2 fs0 fc0 sc0 lsa5">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54">)</span></span></div><div class="t m0 x5d hf y79 ff1 fs0 fc0 sc0 ls54 ws5c">a) <span class="ff2 lsa5">f</span><span class="ws6">(<span class="ff2 ls3">z</span><span class="ws47">) = 3<span class="ff2 ls3">z<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span></span></span>2<span class="ff2 lsa">z</span><span class="ws1">+ 4<span class="_25 blank"> </span>b)<span class="_4 blank"> </span><span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span></span><span class="ws0">) = (1<span class="_6 blank"> </span><span class="ff4 lsb">\u2212</span></span></span>4<span class="ff2 ls3">z<span class="ff3 fs1 ls2f v5">2</span></span>)<span class="ff3 fs1 v5">3</span></span></div><div class="t m0 x5d h2 y7a ff1 fs0 fc0 sc0 ls54 ws5d">c) <span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span></span><span class="ws0">) =<span class="_1 blank"> </span><span class="ff2 lsa v1">z<span class="ff4 lsb">\u2212</span></span><span class="v1">1</span></span></div><div class="t m0 x5e h2c y7b ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls11">z</span><span class="ws5e">+<span class="_6 blank"> </span>1 <span class="ff2 ws5f v1">,<span class="_1d blank"> </span>z <span class="ff4 ws8">6<span class="ff1 ls13">=</span><span class="ls14">\u2212</span></span></span></span><span class="v1">1<span class="ff2 ws5">/<span class="ff1 ws60">2<span class="_26 blank"> </span>d) </span><span class="lsa7">f<span class="ff1 ls2a">(</span><span class="ls7">z</span></span><span class="ff1 ws4e">) = </span><span class="ls3">z<span class="ff3 fs1 ls2f v5">2</span></span><span class="ff1 ws1">(1 + </span><span class="ls3">z</span><span class="ff7 fs1 ws13 v5">\u2212<span class="ff3 ls38">2</span></span></span>)<span class="ff3 fs1 ls2f v5">4</span><span class="ff2 ws5f">,<span class="_1d blank"> </span>z <span class="ff4 ws8">6</span></span><span class="ws0">= 0<span class="ff2">.</span></span></span></div><div class="t m0 x14 h1e y7c ff2 fs0 fc0 sc0 lsa5">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span><span class="ls54 ws5">z<span class="ff6 fs1 lsa8 va">o</span><span class="ff1 ws4e">) = <span class="ff4 ws8">\u2212</span><span class="ws6">1</span></span><span class="ws61">/z <span class="ff3 fs1 v5">2</span></span></span></div><div class="t m0 x3d h2d y7d ff6 fs1 fc0 sc0 lsa9">o<span class="ff2 fs0 lsa7 vb">f<span class="ff1 ls54 ws6">(<span class="ff2 ls3">z</span><span class="ws47">) = 1<span class="ff2 ws62">/z z</span></span></span></span><span class="lsaa v1f">o</span><span class="ff4 fs0 ls54 ws8 vb">6<span class="ff1 ws0">= 0</span></span></div><div class="t m0 x5f hb y7e ff2 fs0 fc0 sc0 lsa5">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws63">) = Re(</span>z<span class="ff1 lsab">)</span><span class="lsa7">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span></span>z<span class="ff1 ls54">)</span></span></div><div class="t m0 x60 h5 y7f ff2 fs0 fc0 sc0 ls54">z</div><div class="t m0 x19 h5 y80 ff2 fs0 fc0 sc0 ls6b">w<span class="ff1 ls18">=</span><span class="lsa7">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54">)</span></span></span></div><div class="t m0 x61 h5 y81 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2">w</span></div><div class="t m0 x62 h20 y82 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsac">z</span><span class="ls1b v1">=</span><span class="ff2 lsa7 v2">f</span><span class="v2">(<span class="ff2 ls11">z</span><span class="ws1">+ \u2206<span class="ff2 ls3">z</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 lsa7">f</span></span><span class="ls2a">(<span class="ff2 ls7">z</span></span></span>)</span></span></div><div class="t m0 x63 h20 y82 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsad">z</span><span class="ls66 v1">=</span><span class="v2">Re<span class="ff4 ws8">{<span class="ff2 ls11">z</span><span class="ff1 ws1">+ \u2206<span class="ff2 ls3">z</span></span><span class="ws64">} \u2212<span class="_3 blank"> </span></span></span>Re<span class="ff4 ls55">{<span class="ff2 ls7">z</span><span class="ls54">}</span></span></span></div><div class="t m0 x52 h20 y82 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsae">z</span><span class="ls1b v1">=</span><span class="ff2 ls8c v2">x</span><span class="ws1 v2">+ \u2206<span class="ff2 ls8c">x<span class="ff4 lsb">\u2212</span><span class="ls54">x</span></span></span></div><div class="t m0 x64 h20 y82 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 ls8c">x</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131</span>\u2206<span class="ff2 lsaf">y</span><span class="lsb0 v1">=</span><span class="v2">\u2206<span class="ff2">x</span></span></div><div class="t m0 x65 h5 y82 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 ls8c">x</span><span class="lse">+</span><span class="ff2 ws5">\u0131</span>\u2206<span class="ff2">y</span></div><div class="t m0 x66 h5 y83 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 ws24">w /</span>\u2206<span class="ff2 ws65">z<span class="_27 blank"> </span>x </span>\u2206<span class="ff2 lsb1">y</span><span class="ws66">= 0<span class="ff2 ls1f">,</span></span>\u2206<span class="ff2 lsb2">x</span><span class="ff4 ws8">6</span><span class="ws66">= 0<span class="_28 blank"> </span>1</span></div><div class="t m0 x67 h5 y84 ff2 fs0 fc0 sc0 lsb3">y<span class="ff1 ls54 ws6">\u2206</span><span class="ls9a">x<span class="ff1 ls54 ws0">= 0</span><span class="ls3a">,<span class="ff1 ls54 ws6">\u2206</span><span class="lsb4">y<span class="ff4 ls54 ws8">6<span class="ff1 ws0">= 0</span></span></span></span></span></div><div class="t m0 x68 h5 y85 ff2 fs0 fc0 sc0 lsa5">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws67">) = <span class="ff2">z</span></span></span></div><div class="t m0 x69 h5 y86 ff2 fs0 fc0 sc0 lsb5">g<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws47">) = Im(</span><span class="ls7">z<span class="ff1 ls54">)</span></span></span></div><div class="t m0 x61 h5 y87 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2">w</span></div><div class="t m0 x62 h3 y88 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsb6">z</span><span class="ls1b v1">=</span><span class="ff2 lsa5 v2">f</span><span class="v2">(<span class="ff2 lsa">z</span><span class="ws1">+ \u2206<span class="ff2 ls7">z</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 lsa5">f</span></span></span></span>(<span class="ff2 ls3">z</span>)</span></div><div class="t m0 x63 h3 y88 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsb7">z</span><span class="lsb8 v1">=</span><span class="v2">Im<span class="ff4 ls55">{<span class="ff2 lsa">z</span></span><span class="ws1">+ \u2206<span class="ff2 ls3">z</span><span class="ff4 ws64">} \u2212<span class="_3 blank"> </span></span></span>Im<span class="ff4 ws8">{<span class="ff2 ls3">z</span>}</span></span></div><div class="t m0 x52 h3 y88 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsb9">z</span><span class="ls1b v1">=</span><span class="ff2 lsba v2">y</span><span class="ws1 v2">+ \u2206<span class="ff2 lsbb">y<span class="ff4 lsb">\u2212</span><span class="ls54">y</span></span></span></div><div class="t m0 x64 h3 y88 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 ls8c">x</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131</span>\u2206<span class="ff2 lsbc">y</span><span class="lsbd v1">=</span><span class="v2">\u2206<span class="ff2">y</span></span></div><div class="t m0 x65 h5 y88 ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 ls8c">x</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131</span>\u2206<span class="ff2">y</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w3 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg5.png"><div class="t m0 x51 h5 y29 ff2 fs0 fc0 sc0 ls54 ws24">dw /dz</div><div class="t m0 xe h5 y2a ff2 fs0 fc0 sc0 ls54">w</div><div class="t m0 xe hb y89 ff2 fs0 fc0 sc0 lsbe">w<span class="ff1 ls13">=</span><span class="ls54 ws68">z<span class="_29 blank"> </span>w <span class="ff1 ls13">=</span><span class="ls11">z<span class="ff4 lsb">\u2212</span></span>z<span class="_2a blank"> </span>w <span class="ff1 ws0">= 2</span><span class="ls8b">x<span class="ff1 lse">+</span></span><span class="ws69">xy <span class="ff3 fs1 ls38 v5">2</span><span class="ws6a">\u0131<span class="_7 blank"> </span>w <span class="ff1 ws0">= e<span class="ff6 fs1 lsbf v5">x</span><span class="ff4 ws8">{</span><span class="ws6">cos(</span></span><span class="ls8e">y<span class="ff1 ls39">)<span class="ff4 ls27">\u2212</span></span><span class="ls52">\u0131</span></span><span class="ff1 ws6">sen(</span><span class="ls8e">y<span class="ff1 ls2a">)</span></span><span class="ff4">}</span></span></span></span></div><div class="t m0 x6a hb y8a ff2 fs0 fc0 sc0 lsa5">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54">)</span></span></div><div class="t m0 x1a hb y8b ff2 fs0 fc0 sc0 lsa7">f<span class="ff7 fs1 ls54 ws6b v5">00 </span><span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 lsc0">)</span><span class="lsa5">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span></span>z<span class="ff1 lsc1">)</span></span>f<span class="ff7 fs1 ls54 ws6b v5">00 </span><span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54">)</span></span></div><div class="t m0 x6b hb y8c ff2 fs0 fc0 sc0 lsa5">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws0">) =<span class="_1 blank"> </span>lim</span></span></div><div class="t m0 x29 h2e y8d ff3 fs1 fc0 sc0 lsc2">\u2206<span class="ff6 lsc3">z<span class="ff7 ls54 ws13">\u2192<span class="ff3">0</span></span></span></div><div class="t m0 x6c h5 y8e ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2">f</span></div><div class="t m0 x6c h3 y8f ff1 fs0 fc0 sc0 ls54 ws6">\u2206<span class="ff2 lsc4">z</span><span class="ls1b v1">=</span><span class="ff2 ws6c v2">\u2202 u</span></div><div class="t m0 x6d h3 y8f ff2 fs0 fc0 sc0 ls54 ws6c">\u2202 x<span class="_a blank"> </span><span class="ff1 ls2e v1">+</span><span class="lsc5 v1">\u0131</span><span class="v2">\u2202 v</span></div><div class="t m0 x6e h2f y8f ff2 fs0 fc0 sc0 ls54 ws6c">\u2202 x<span class="_3 blank"> </span><span class="ff1 v1">:</span></div><div class="t m0 x5d hb y90 ff1 fs0 fc0 sc0 ls54 ws5c">a) <span class="ff2 lsa5">f</span><span class="ws6">(<span class="ff2 ls3">z</span><span class="ws67">) = <span class="ff2 ws6d">\u0131z </span><span class="ws1">+ 2<span class="_26 blank"> </span>b)<span class="_4 blank"> </span><span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span><span class="lsc6 ws6e">)=e<span class="_2b blank"></span><span class="ff7 fs1 ls54 ws13 v5">\u2212<span class="ff6 lsbf">x<span class="ff4 fs0 ls55 v20">{<span class="ff1 ls54 ws6">cos(<span class="ff2 ls91">y</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span>sen(<span class="ff2 ls91">y</span>)<span class="ff4">}</span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x5d h10 y91 ff1 fs0 fc0 sc0 ls54 ws5d">c) <span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span></span><span class="ws4e">) = <span class="ff2 ls3">z<span class="ff3 fs1 lsc7 v5">3</span></span><span class="ws6f">d) <span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span></span><span class="ws0">) = cos(<span class="ff2 ls8d">x</span><span class="ws23">) cosh(<span class="ff2 ls91">y</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span><span class="ws6">sen(<span class="ff2 ls8d">x</span></span>) senh(<span class="ff2 ls8e">y</span>)</span></span></span></span></div><div class="t m0 x11 h10 y92 ff2 fs0 fc0 sc0 ls6b">w<span class="ff1 ls18">=</span><span class="ls7">z<span class="ff3 fs1 ls36 v5">3</span><span class="ff1 ls54 ws0">= (</span><span class="ls8c">x<span class="ff1 ls2e">+</span><span class="ls54 ws70">\u0131y <span class="ff1 ws6">)<span class="ff3 fs1 ls1c v5">3</span><span class="ls18">=</span></span><span class="ls8d">x<span class="ff3 fs1 ls45 v5">3</span></span><span class="ff1 ws1">+ 3</span><span class="ls8d">x<span class="ff3 fs1 ls38 v5">2</span></span><span class="ff1 ws6">(</span>\u0131y </span><span class="ff1 ls1 ws2">)+3<span class="_2 blank"></span><span class="ff2 ls8d">x<span class="ff1 ls54 ws6">(<span class="ff2 ws70">\u0131y </span>)<span class="ff3 fs1 ls45 v5">2</span><span class="ws1">+ (<span class="ff2 ws4f">\u0131y </span><span class="ls2a">)<span class="ff3 fs1 ls1c v5">3</span><span class="ls13">=</span></span></span></span>x<span class="ff3 fs1 ls45 v5">3</span><span class="ff4 ls27">\u2212<span class="ff1 ls54 ws6">3<span class="ff2 ws69">xy <span class="ff3 fs1 ls45 v5">2</span></span><span class="lse">+</span><span class="ff2 ws5">\u0131</span>(3</span></span>x<span class="ff3 fs1 ls2f v5">2</span><span class="lsbb">y<span class="ff4 lsb">\u2212</span><span class="ls8e">y<span class="ff3 fs1 ls38 v5">3</span><span class="ff1 ls54 ws67">) = </span><span class="lsc8">u<span class="ff1 lse">+</span><span class="ls54">\u0131v</span></span></span></span></span></span></span></span></div><div class="t m0 x11 h10 y93 ff2 fs0 fc0 sc0 lsc9">u<span class="ff1 lsca">=</span><span class="ls8d">x<span class="ff3 fs1 lscb v5">3</span><span class="ff4 lscc">\u2212<span class="ff1 ls54 ws6">3</span></span><span class="ls54 ws71">xy <span class="ff3 fs1 lscd v5">2</span><span class="lsce">v</span><span class="ff1 ws72">= 3</span></span>x<span class="ff3 fs1 ls38 v5">2</span><span class="lscf">y<span class="ff4 lscc">\u2212</span><span class="ls91">y<span class="ff3 fs1 lsd0 v5">3</span><span class="ls54 ws11">u, v<span class="_2c blank"> </span>, u<span class="ff6 fs1 lsbf va">x</span>, u<span class="ff6 fs1 lsd1 va">y</span>, v<span class="ff6 fs1 lsbf va">x</span>, v<span class="ff6 fs1 va">y</span></span></span></span></span></div><div class="t m0 x1b h10 y94 ff8 fs0 fc0 sc0 ls54 ws73">R<span class="ff3 fs1 v5">2</span></div><div class="t m0 x6f h10 y95 ff2 fs0 fc0 sc0 ls54 ws5">u<span class="ff6 fs1 lsd2 va">x</span><span class="ff1 ws0">= 3</span><span class="ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span></span><span class="ff1 ws6">3</span><span class="ls91">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls13">=</span><span class="lsd3">v<span class="ff6 fs1 lsd4 va">y</span></span></span>u<span class="ff6 fs1 lsd5 va">y</span><span class="ff1 ls13">=<span class="ff4 ls14">\u2212</span><span class="ls54 ws6">6</span></span><span class="ws52">xy <span class="ff1 ls18">=</span><span class="ff4 ws8">\u2212</span><span class="lsd3">v</span><span class="ff6 fs1 va">x</span></span></div><div class="t m0 x11 h10 y96 ff2 fs0 fc0 sc0 ls6b">w<span class="ff1 ls18">=</span><span class="ls7">z<span class="ff3 fs1 ls54 v5">3</span></span></div><div class="t m0 x68 h5 y97 ff2 fs0 fc0 sc0 ls54">dw</div><div class="t m0 x68 h30 y98 ff2 fs0 fc0 sc0 ls54 ws74">dz <span class="ff1 ls13 v1">=</span><span class="lsd6 v1">u</span><span class="ff6 fs1 lsd7 v1e">x</span><span class="ff1 ls2e v1">+</span><span class="ws5 v1">\u0131v</span><span class="ff6 fs1 lsd2 v1e">x</span><span class="ff1 ws0 v1">= 3</span><span class="ls8d v1">x</span><span class="ff3 fs1 ls45 v3">2</span><span class="ff4 ls27 v1">\u2212</span><span class="ff1 ws6 v1">3</span><span class="ls8e v1">y</span><span class="ff3 fs1 ls45 v3">2</span><span class="ff1 ws1 v1">+ 6</span><span class="ws46 v1">xy \u0131<span class="_4 blank"> </span><span class="ff1 ws0">= 3(<span class="ff2 ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span><span class="ls91">y<span class="ff3 fs1 ls2f v5">2</span></span></span><span class="ls1 ws2">)+6<span class="_2 blank"></span><span class="ff2 ls54 ws46">xy \u0131<span class="_4 blank"> </span><span class="ff1 ws0">= 3</span><span class="ls3">z</span><span class="ff3 fs1 v5">2</span></span></span></span></span></div><div class="t m0 x70 h5 y99 ff2 fs0 fc0 sc0 ls54 ws24">dw /dz<span class="_f blank"> </span>u<span class="ff6 fs1 lsd8 va">x</span><span class="ws5">v<span class="ff6 fs1 va">x</span></span></div><div class="t m0 x10 h10 y9a ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 ws5">u<span class="ff6 fs1 lsbf va">x</span></span><span class="ls2a">)<span class="ff6 fs1 lsd9 va">x</span><span class="lsda">=<span class="ff2 lsd6">u</span></span></span><span class="ff6 fs1 ws75 va">xx </span><span class="ff2 ls1f">,</span>(<span class="ff2 lsd6">u<span class="ff6 fs1 lsbf va">x</span></span>)<span class="ff6 fs1 lsdb va">y</span><span class="lsda">=<span class="ff2 lsd6">u</span></span><span class="ff6 fs1 ws76 va">xy </span><span class="ff2 ls1f">,</span>(<span class="ff2 ws5">v<span class="ff6 fs1 lsbf va">x</span></span><span class="ls2a">)<span class="ff6 fs1 lsd9 va">x</span><span class="lsda">=<span class="ff2 lsd3">v</span></span></span><span class="ff6 fs1 ws75 va">xx </span><span class="ff2 ls1f">,</span>(<span class="ff2 ws5">v<span class="ff6 fs1 lsbf va">x</span></span><span class="ls2a">)<span class="ff6 fs1 lsdb va">y</span><span class="lsda">=</span></span><span class="ff2 ws5">v<span class="ff6 fs1 ws77 va">xy </span><span class="ff8 ws73">R<span class="ff3 fs1 v5">2</span></span></span></div><div class="t m0 x71 h5 y9b ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 lsd6">u<span class="ff6 fs1 lsbf va">x</span></span>)<span class="ff6 fs1 lsd2 va">x</span><span class="ls13">=<span class="ff2 lsd6">u</span></span><span class="ff6 fs1 ws78 va">xx </span><span class="ws0">= 6<span class="ff2 ls9a">x</span>= (<span class="ff2 ws5">v<span class="ff6 fs1 lsbf va">x</span></span></span>)<span class="ff6 fs1 lsdc va">y</span>(<span class="ff2 lsd6">u<span class="ff6 fs1 lsbf va">x</span></span>)<span class="ff6 fs1 lsd5 va">y</span><span class="ls13">=<span class="ff4 ls14">\u2212</span></span>6<span class="ff2 lsb4">y</span><span class="ls13">=<span class="ff4 ls14">\u2212</span></span><span class="ff2 ws5">v<span class="ff6 fs1 ws79 va">xy </span></span><span class="ls13">=<span class="ff4 ls14">\u2212</span></span>(<span class="ff2 ws5">v<span class="ff6 fs1 lsbf va">x</span></span><span class="ls2a">)</span><span class="ff6 fs1 va">y</span></div><div class="t m0 x72 h5 y9c ff2 fs0 fc0 sc0 ls54 ws24">dw /dz</div><div class="t m0 x16 h31 y9d ff2 fs0 fc0 sc0 lsdd">d<span class="ff3 fs1 ls2f v4">2</span><span class="ls54">w</span></div><div class="t m0 x1 h3 y9e ff2 fs0 fc0 sc0 ls54 ws7a">dz <span class="ff3 fs1 lsde v6">2</span><span class="ff1 lsdf v1">=</span><span class="v2">d</span></div><div class="t m0 x1b h3 y9e ff2 fs0 fc0 sc0 ls54 ws7b">dz <span class="ff1 ls60 v1">(</span><span class="v2">dw</span></div><div class="t m0 x73 h3 y9e ff2 fs0 fc0 sc0 ls54 ws7c">dz <span class="ff1 ws0 v1">) =<span class="_1 blank"> </span></span><span class="v2">d</span></div><div class="t m0 x5e h2f y9e ff2 fs0 fc0 sc0 ls54 ws7d">dz <span class="ff1 ls2a v1">(</span><span class="ws5 v1">u</span><span class="ff6 fs1 lsd7 v1e">x</span><span class="ff1 ls2e v1">+</span><span class="ws5 v1">\u0131v</span><span class="ff6 fs1 lsbf v1e">x</span><span class="ff1 lsc6 ws6e v1">)=(<span class="_2b blank"></span><span class="ff2 lsd6">u<span class="ff6 fs1 lsbf va">x</span><span class="ff1 ls54 ws6">)<span class="ff6 fs1 lsd7 va">x</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131</span>(</span><span class="lsd3">v<span class="ff6 fs1 lsbf va">x</span><span class="ff1 ls54 ws6">)<span class="ff6 fs1 lsd2 va">x</span><span class="ls13">=</span></span></span>u<span class="ff6 fs1 ls54 ws7e va">xx </span><span class="ff1 lse">+</span><span class="ls54 ws5">\u0131v<span class="ff6 fs1 ws78 va">xx </span><span class="ff1 ws0">= 6</span><span class="ls8c">x</span><span class="ff1 ws1">+ 6</span><span class="ws46">y \u0131<span class="_4 blank"> </span><span class="ff1 ws0">= 6(</span><span class="ls8c">x<span class="ff1 ls2e">+</span></span><span class="ws70">\u0131y <span class="ff1 ws47">) = 6</span>z</span></span></span></span></span></div><div class="t m0 x68 hb y9f ff2 fs0 fc0 sc0 ls54 ws7f">z<span class="_2d blank"> </span>f <span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls2a">(</span><span class="ls7">z</span><span class="ff1">)</span></div><div class="t m0 xe hf ya0 ff2 fs0 fc0 sc0 lsa5">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws47">) = 1</span><span class="ls54 ws7f">/z<span class="_29 blank"> </span>f <span class="ff1 ws6">(</span></span>z<span class="ff1 ls54 ws4e">) = </span><span class="ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls2e">+</span><span class="ls54 ws70">\u0131y <span class="ff3 fs1 ls69 v5">2</span></span></span></span>f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws67">) = </span><span class="lse0">z<span class="ff1 ls54 ws6">Im(</span><span class="ls7">z<span class="ff1 ls54">)</span></span></span></span></div><div class="t m0 x74 hb ya1 ff2 fs0 fc0 sc0 lsa5">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws67">) = </span>z<span class="ff3 fs1 ls54 ws3d v5">1<span class="ff6 ws20">/<span class="ff3">2</span></span></span></span></div><div class="t m0 x17 h32 ya2 ff2 fs0 fc0 sc0 lsa7">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws4e">) = <span class="ff4 ws8 v13">\u221a</span></span><span class="lse1">r<span class="ff4 ls55">{<span class="ff1 ls54 ws6">cos(</span></span><span class="ls54 ws24">\u03b8 /<span class="ff1 ws1">2) + </span><span class="ls52">\u0131</span><span class="ff1 ws6">sen(</span>\u03b8 /<span class="ff1 ws6">2)<span class="ff4">}</span></span></span></span></span></div><div class="t m0 x75 h1e ya3 ff2 fs0 fc0 sc0 lse2">z<span class="ff1 lse3">=</span><span class="lse4">r<span class="ff4 ls54 ws8">{<span class="ff1 ws6">cos(</span></span><span class="ls48">\u03b8<span class="ff1 ls54 ws80">) + </span><span class="ls52">\u0131<span class="ff1 ls54 ws6">sen(</span></span>\u03b8<span class="ff1 ls2a">)<span class="ff4 lse5">}</span></span><span class="ls54 ws81">r<span class="_3 blank"> </span>> <span class="ff1 ws82">0<span class="_2e blank"> </span>0 <span class="ff4 lse6">\u2264</span></span><span class="ws83">\u03b8<span class="_3 blank"> </span>< <span class="ff1 ws6">2</span><span class="ws7f">\u03c0<span class="_2f blank"> </span>f <span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls2a">(</span><span class="ls7">z</span><span class="ff1">)</span></span></span></span></span></span></div><div class="t m0 x76 h2 ya4 ff2 fs0 fc0 sc0 lsa5">f<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws0">) =<span class="_30 blank"> </span><span class="v1">1</span></span></span></div><div class="t m0 xb h5 ya5 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span></span>)</div><div class="t m0 x74 h2 ya6 ff2 fs0 fc0 sc0 lsa7">f<span class="ff1 ls2a">(</span><span class="ls7">z<span class="ff1 ls54 ws4e">) = </span><span class="ls8d">x<span class="ff3 fs1 lse7 v5">3</span><span class="ff4 lse8">\u2212</span><span class="ls54 ws5">\u0131<span class="ff1 ls2a">(</span><span class="lse9">y<span class="ff4 lse8">\u2212</span></span><span class="ff1 ws6">1)<span class="ff3 fs1 lsea v5">3</span></span><span class="ws6c v1">\u2202 u</span></span></span></span></div><div class="t m0 x77 h3 ya7 ff2 fs0 fc0 sc0 ls54 ws6c">\u2202 x<span class="_6 blank"> </span><span class="ff1 lseb v1">+</span><span class="lsec v1">\u0131</span><span class="v2">\u2202 v</span></div><div class="t m0 x78 h2c ya7 ff2 fs0 fc0 sc0 ls54 ws6c">\u2202 x<span class="_3 blank"> </span><span class="ff1 ws0 v1">= 3</span><span class="ls8d v1">x</span><span class="ff3 fs1 lsed v3">2</span><span class="ff1 ws6 v1">3</span><span class="ls8d v1">x</span><span class="ff3 fs1 lsee v3">2</span><span class="lsa5 v1">f</span><span class="ff7 fs1 lsa6 v3">0</span><span class="ff1 ws6 v1">(</span><span class="ls3 v1">z<span class="ff1 lsef">)<span class="ff2 ls23">z</span><span class="ls18">=</span></span></span><span class="v1">\u0131</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w3 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg6.png"><div class="t m0 x79 h5 y6b ff1 fs0 fc0 sc0 ls54 ws5c">a) <span class="ff2 lsa7">f</span><span class="ls2a">(<span class="ff2 ls7">z</span><span class="lsc6 ws6e">)=3<span class="_2b blank"></span><span class="ff2 ls8c">x<span class="ff1 ls2e">+</span><span class="lsba">y<span class="ff1 lse">+</span><span class="ls54 ws5">\u0131<span class="ff1 ws6">(3</span></span>y<span class="ff4 lsb">\u2212</span><span class="ls8d">x<span class="ff1 ls54 ws84">)<span class="_31 blank"> </span>b) </span><span class="lsa7">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws0">) =<span class="_1d blank"> </span>sen(</span></span></span>x<span class="ff1 ls54 ws23">) cosh(</span><span class="ls91">y<span class="ff1 ls54 ws1">) + </span><span class="ls31">\u0131<span class="ff1 ls54 ws6">cos(</span></span></span>x<span class="ff1 ls54 ws23">) senh(</span><span class="ls91">y<span class="ff1 ls54">)</span></span></span></span></span></span></span></div><div class="t m0 x79 hb ya8 ff1 fs0 fc0 sc0 ls54 ws5d">c) <span class="ff2 lsa7">f</span><span class="ws6">(<span class="ff2 ls3">z</span><span class="ws0">) =<span class="_1d blank"> </span>e<span class="ff7 fs1 ws13 v5">\u2212<span class="ff6 lsf0">y</span></span><span class="ff4 ls55">{</span></span>cos(<span class="ff2 ls8d">x</span><span class="ws1">) + <span class="ff2 ls52">\u0131</span></span>sen(<span class="ff2 ls8d">x</span>)<span class="ff4 lsf1">}</span><span class="ws85">d) <span class="ff2 lsa7">f</span></span>(<span class="ff2 ls3">z</span><span class="ws47">) = (<span class="ff2 ls3">z<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212</span></span><span class="ws23">2) e<span class="ff7 fs1 ls29 v5">\u2212<span class="ff6 lsbf">x</span></span><span class="ff4 ws8">{</span></span></span>cos(<span class="ff2 ls8e">y</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls31">\u0131</span></span></span>sen(<span class="ff2 ls8e">y</span><span class="ls2a">)</span><span class="ff4">}</span></span></div><div class="t m0 x22 h1e ya9 ff1 fs0 fc0 sc0 lsf2">e<span class="ff7 fs1 ls54 ws13 v5">\u2212<span class="ff6 lsbf">x</span></span><span class="ff4 ls55">{</span><span class="ls54 ws6">cos(<span class="ff2 ls91">y</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls52">\u0131</span></span></span>sen(<span class="ff2 ls91">y</span>)<span class="ff4 lsf3">}</span><span class="ws86">= e<span class="ff7 fs1 ls29 v5">\u2212<span class="ff6 lsbf">x</span></span><span class="ff4 ws8">{</span></span>cos(<span class="ff4 ws8">\u2212<span class="ff2 ls91">y</span></span><span class="ws1">) + <span class="ff2 ls52">\u0131</span></span>sen(<span class="ff4 ls14">\u2212<span class="ff2 ls8e">y</span></span><span class="ls2a">)<span class="ff4 lsf3">}</span></span><span class="ws86">= e<span class="ff7 fs1 ws13 v5">\u2212<span class="ff6 lsf4">x</span></span></span>exp(<span class="ff2 ws5">\u0131</span>(<span class="ff4 ls14">\u2212<span class="ff2 ls91">y</span></span><span class="ws47">)) = exp(<span class="ff4 ws8">\u2212<span class="ff2 ls8c">x</span><span class="lsb">\u2212</span><span class="ff2 ws70">\u0131y </span></span>) = exp(<span class="ff4 ls14">\u2212<span class="ff2 ls7">z</span></span>)</span></span></div><div class="t m0 x16 hf yaa ff2 fs0 fc0 sc0 lsa5">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws47">) = (</span><span class="ls7">z<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212<span class="ff1 ls54 ws23">2) exp(</span><span class="ls54 ws8">\u2212</span></span></span>z<span class="ff1 ls54">)</span></span></div><div class="t m0 xe hb yab ff2 fs0 fc0 sc0 lsa7">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws4e">) = </span><span class="ls54 ws87">xy <span class="ff1 ls2e">+</span><span class="ws88">\u0131y<span class="_29 blank"> </span>f <span class="ff1 ws6">(</span></span></span>z<span class="ff1 ls54 ws0">) =<span class="_1d blank"> </span>e<span class="ff6 fs1 lsd1 v5">y</span><span class="ff4 ls55">{</span><span class="ws6">cos(</span></span><span class="ls8d">x<span class="ff1 ls54 ws1">) + </span><span class="ls52">\u0131<span class="ff1 ls54 ws6">sen(</span></span>x<span class="ff1 ls54 ws6">)<span class="ff4">}</span></span></span></span></div><div class="t m0 xe h2 yac ff2 fs0 fc0 sc0 lsa7">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 ws0">) =<span class="_32 blank"> </span><span class="ws6 v1">2</span></span><span class="ls11 v1">z<span class="ff1 ls54 ws1">+ 1</span></span></span></div><div class="t m0 x7a h33 yad ff2 fs0 fc0 sc0 ls3">z<span class="ff1 ls54 ws6">(</span>z<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls54 ws1">+ 1)<span class="_33 blank"> </span></span><span class="lsa5 v1">f<span class="ff1 ls54 ws6">(</span></span><span class="v1">z<span class="ff1 ls54 ws0">) =<span class="_34 blank"> </span></span><span class="v1">z</span></span><span class="ff3 fs1 ls45 v21">3</span><span class="ff1 ls2e v2">+</span><span class="ls54 v2">\u0131</span></div><div class="t m0 x7b h34 yad ff2 fs0 fc0 sc0 ls7">z<span class="ff3 fs1 ls45 v6">2</span><span class="ff4 ls27">\u2212<span class="ff1 ls54 ws6">3</span></span><span class="lsa">z<span class="ff1 ls54 ws1">+ 2<span class="_7 blank"> </span></span><span class="lsa7 v1">f<span class="ff1 ls2a">(</span></span></span><span class="v1">z<span class="ff1 lsc6 ws6e">)=(<span class="_2b blank"></span><span class="ff2 lsa">z<span class="ff1 ls54 ws1">+ 2)<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls2f">1</span></span><span class="ws6">(</span></span><span class="ls3">z<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls54 ws1">+ 2</span></span>z<span class="ff1 ls54 ws1">+ 2)<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls54">1</span></span></span></span></span></span></div><div class="t m0 x16 h5 yae ff2 fs0 fc0 sc0 ls23">z<span class="ff1 ls18">=</span><span class="lsf5">r<span class="ff4 ls55">{<span class="ff1 ls54 ws6">cos(</span></span><span class="ls10">\u03b8<span class="ff1 ls54 ws1">) + </span><span class="ls52">\u0131<span class="ff1 ls54 ws6">sen(</span><span class="ls48">\u03b8<span class="ff1 ls2a">)<span class="ff4 ls54">}</span></span></span></span></span></span></div><div class="t m0 x2b h2 yaf ff2 fs0 fc0 sc0 lsf6">F<span class="ff1 ls2a">(</span><span class="ls7">z<span class="ff1 ls54 ws0">) = ln(</span><span class="lse4">r<span class="ff1 ls54 ws1">) + </span><span class="ls54 ws24">\u0131\u03b8 ,<span class="_b blank"> </span>r<span class="_a blank"> </span>><span class="_4 blank"> </span><span class="ff1 ws6">0</span><span class="lsf7">,<span class="ff4 lsf8">\u2212</span></span><span class="v1">\u03c0</span></span></span></span></div><div class="t m0 x7c h20 yb0 ff1 fs0 fc0 sc0 lsf9">2<span class="ff2 ls54 ws89 v1">< \u03b8<span class="_a blank"> </span><<span class="_3 blank"> </span><span class="v1">\u03c0</span></span></div><div class="t m0 x7d h5 yb0 ff1 fs0 fc0 sc0 ls54">2</div><div class="t m0 x5f hb yb1 ff2 fs0 fc0 sc0 lsf6">F<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls2a">(</span><span class="ls7">z<span class="ff1 ls54 ws8a">) = 1<span class="ff2">/z</span></span></span></div><div class="t m0 x7a h5 yb2 ff2 fs0 fc0 sc0 ls54 ws5">G<span class="ff1 ws6">(</span><span class="ls3">z</span><span class="ff1 ws67">) = </span><span class="lsfa">F</span><span class="ff1 ws6">(2</span><span class="lsa">z<span class="ff1 lse">+</span><span class="lsfb">\u0131<span class="ff4 lsb">\u2212</span></span></span><span class="ff1 ws8b">2) </span><span class="ws56">z<span class="_35 blank"> </span>x > <span class="ff1">1</span></span></div><div class="t m0 x74 h5 yb3 ff2 fs0 fc0 sc0 lsbe">w<span class="ff1 ls13">=</span><span class="lsfc">u<span class="ff1 lsfd">+</span><span class="ls54 ws8c">\u0131v <span class="ff4 ws8">\u2212</span><span class="lsfe">v<span class="ff1 lsfd">+</span></span><span class="ws8d">\u0131u u</span></span></span></div><div class="t m0 x7e h5 yb4 ff2 fs0 fc0 sc0 ls54 ws8e">v<span class="_36 blank"> </span>u <span class="ff4 ws8">\u2212</span>v</div><div class="t m0 x12 h5 yb5 ff2 fs0 fc0 sc0 ls54 ws8f">u v</div><div class="t m0 xe h1e yb6 ff2 fs0 fc0 sc0 lsff">u<span class="ff1 ls54 ws0">= 2</span><span class="ls8d">x<span class="ff1 ls54 ws12">(1 <span class="ff4 lsb">\u2212</span></span><span class="ls91">y<span class="ff1 ls100">)</span><span class="ls101">u<span class="ff1 ls54 ws0">= 2</span><span class="ls8b">x<span class="ff4 ls27">\u2212</span></span></span></span>x<span class="ff3 fs1 ls45 v5">3</span><span class="ff1 ls54 ws1">+ 3</span><span class="ls54 ws71">xy <span class="ff3 fs1 ls69 v5">2</span></span></span>u<span class="ff1 ls54 ws86">= senh(</span><span class="ls8d">x<span class="ff1 ls54 ws23">) sen(</span><span class="ls91">y<span class="ff1 ls100">)</span><span class="ls101">u<span class="ff1 ls13">=</span></span>y<span class="ff1 ls54 ws6">(</span><span class="ls8f">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 ls2e">+</span><span class="ls8e">y<span class="ff3 fs1 ls38 v5">2</span><span class="ff1 ls54 ws6">)<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls54">1</span></span></span></span></span></span></span></div><div class="t m0 x60 h5 yb7 ff2 fs0 fc0 sc0 ls54 ws90">u<span class="_37 blank"> </span>v<span class="_38 blank"> </span>u <span class="ff1 ls18">=</span><span class="ws91">c<span class="_37 blank"> </span>v <span class="ff1 ls18">=</span>d</span></div><div class="t m0 x60 h5 yb8 ff2 fs0 fc0 sc0 ls54 ws92">c d</div><div class="t m0 x3e h5 yb9 ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 ls8d">x<span class="ff6 fs1 ls102 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 ls102 va">o</span></span></span><span class="ls103">)<span class="ff2 ls104">u</span><span class="ls105">=</span></span><span class="ff2 ws93">c<span class="_39 blank"> </span>v </span><span class="ls105">=</span><span class="ff2">d</span></div><div class="t m0 x7f h2e yba ff6 fs1 fc0 sc0 ls54 ws94">\u2202 u</div><div class="t m0 x7f h2e ybb ff6 fs1 fc0 sc0 ls54 ws94">\u2202 x</div><div class="t m0 x4c h2e ybc ff6 fs1 fc0 sc0 ls54 ws94">\u2202 u</div><div class="t m0 x4c h2e ybb ff6 fs1 fc0 sc0 ls54 ws94">\u2202 y</div><div class="t m0 x60 h1a ybd ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 ls8d">x<span class="ff6 fs1 lsa8 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 lsa8 va">o</span></span></span><span class="ls106">)</span><span class="ff6 fs1 v5">dw</span></div><div class="t m0 x80 h14 ybe ff6 fs1 fc0 sc0 ls54 ws95">dz <span class="ff4 fs0 ws8 v4">6<span class="ff1 ws0">= 0<span class="_3a blank"> </span><span class="ff2 ls1a">z</span><span class="ls13">=</span><span class="ff2 ws5">z</span></span></span><span class="ls107 v22">o</span><span class="ff2 fs0 ws5 v4">z</span><span class="lsaa v22">o</span><span class="ff1 fs0 ls18 v4">=<span class="ff2 ls8d">x</span></span><span class="ls108 v22">o</span><span class="ff1 fs0 ls2e v4">+<span class="ff2 ls54 ws5">\u0131y</span></span><span class="ls109 v22">o</span><span class="ff2 fs0 lsbe v4">w<span class="ff1 ls13">=<span class="ff2 lsc8">u</span><span class="lse">+<span class="ff2 ls54">\u0131v</span></span></span></span></div><div class="t m0 x33 h5 ybf ff2 fs0 fc0 sc0 ls54 ws96">u<span class="_3b blank"> </span>v<span class="_3c blank"> </span>w <span class="ff1 ls10a">=</span><span class="ls10b">u<span class="ff1 ls10c">+</span></span><span class="ws97">\u0131v<span class="_3d blank"> </span>u v</span></div><div class="t m0 x43 h5 yc0 ff2 fs0 fc0 sc0 ls54 ws5">u<span class="ff6 fs1 lsd2 va">x</span><span class="ff1 ls18">=</span>v<span class="ff6 fs1 lsd4 va">y</span><span class="lsd6">u<span class="ff6 fs1 ls10d va">y</span><span class="ff1 ls18">=</span></span><span class="ff4 ws8">\u2212</span><span class="lsd3">v</span><span class="ff6 fs1 va">x</span></div><div class="t m0 x81 h5 yc1 ff4 fs0 fc0 sc0 ls54 ws8">\u2207<span class="ff2 ls10e">u<span class="ff1 ls10f">=</span><span class="lsd6">u<span class="ff6 fs1 lsbf va">x</span><span class="ff9 ls110">i<span class="ff1 ls111">+</span></span><span class="ls54 ws5">u<span class="ff6 fs1 lsf0 va">y</span><span class="ff9 ls112">j</span><span class="ff1 ws6">(</span><span class="ls8d">x<span class="ff6 fs1 lsa8 va">o</span></span><span class="ws11">, y<span class="ff6 fs1 lsa8 va">o</span><span class="ff1">)</span></span></span></span></span></div><div class="t m0 x1a h5 yc2 ff4 fs0 fc0 sc0 ls21">\u2207<span class="ff2 ls54 ws5">u<span class="ff1 ls2a">(</span><span class="ls8d">x<span class="ff6 fs1 lsa8 va">o</span></span><span class="ws11">, y<span class="ff6 fs1 lsa8 va">o</span><span class="ff1 ls113">)</span><span class="ls114">u</span><span class="ff1 ws6">(</span><span class="ls8d">x<span class="ff6 fs1 lsa8 va">o</span></span>, y<span class="ff6 fs1 lsa8 va">o</span><span class="ff1">)</span></span></span></div><div class="t m0 x18 h5 yc3 ff2 fs0 fc0 sc0 ls115">u<span class="ff1 ls116">=</span><span class="ls54 ws98">c<span class="_3b blank"> </span>v <span class="ff1 ls116">=</span><span class="ls117">d</span><span class="ff1 ws6">(</span><span class="ls8d">x<span class="ff6 fs1 lsa8 va">o</span></span><span class="ws11">, y<span class="ff6 fs1 lsa8 va">o</span><span class="ff1 ls118">)</span>u</span></span></div><div class="t m0 x1a h5 yc4 ff2 fs0 fc0 sc0 ls119">v<span class="ff1 ls2a">(</span><span class="ls8d">x<span class="ff6 fs1 lsa8 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 lsa8 va">o</span><span class="ff1">)</span></span></span></div><div class="t m0 x82 h5 yc5 ff4 fs0 fc0 sc0 ls21">\u2207<span class="ff2 lsc8">u</span><span class="ls54 ws64">· \u2207<span class="ff2 ls11a">v</span><span class="ff1 ws0">= (<span class="ff2 lsd6">u<span class="ff6 fs1 lsbf va">x</span><span class="ff9 lsfb">i</span></span><span class="lse">+</span><span class="ff2 ws5">u<span class="ff6 fs1 lsf0 va">y</span><span class="ff9 ws73">j</span></span><span class="ls39">)</span></span><span class="ls11b">·</span><span class="ff1 ws6">(<span class="ff2 lsd3">v<span class="ff6 fs1 lsbf va">x</span><span class="ff9 lsfb">i</span></span><span class="lse">+</span><span class="ff2 ws5">v<span class="ff6 fs1 lsf0 va">y</span><span class="ff9 ws73">j</span></span><span class="ws4e">) = <span class="ff2 ws5">u<span class="ff6 fs1 lsbf va">x</span><span class="lsd3">v<span class="ff6 fs1 ls11c va">x</span></span></span><span class="lse">+</span><span class="ff2 ws5">u<span class="ff6 fs1 lsf0 va">y</span>v<span class="ff6 fs1 lsd5 va">y</span></span><span class="ls13">=<span class="ff2 lsd3">v<span class="ff6 fs1 lsd1 va">y</span>v<span class="ff6 fs1 ls11c va">x</span></span></span></span></span><span class="ls27">\u2212</span><span class="ff2 ws5">v<span class="ff6 fs1 lsbf va">x</span>v<span class="ff6 fs1 lsd5 va">y</span><span class="ff1 ws0">= 0</span></span></span></div><div class="t m0 x83 h5 yc6 ff2 fs0 fc0 sc0 ls54 ws24">dw /dz<span class="_a blank"> </span><span class="ff4 ws8">6<span class="ff1 ws0">= 0<span class="_3a blank"> </span></span></span><span class="ws5">z<span class="ff6 fs1 lsaa va">o</span><span class="ff1 ls18">=</span><span class="ls8d">x<span class="ff6 fs1 ls11d va">o</span><span class="ff1 ls11e">+</span></span>\u0131y<span class="ff6 fs1 va">o</span></span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w3 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg7.png"><div class="t m0 x74 h10 y29 ff2 fs0 fc0 sc0 ls6b">w<span class="ff1 ls18">=</span><span class="ls11f">u<span class="ff1 ls120">+</span><span class="ls54 ws91">\u0131v <span class="ff1 ls18">=</span><span class="ls7">z<span class="ff3 fs1 ls121 v5">2</span></span><span class="ws99">u v</span></span></span></div><div class="t m0 x84 h5 y2a ff2 fs0 fc0 sc0 ls122">c<span class="ff4 ls54 ws8">6<span class="ff1 ws9a">= 0<span class="_3e blank"> </span></span></span><span class="ls123">d<span class="ff4 ls54 ws8">6<span class="ff1 ws9a">= 0<span class="_3f blank"> </span></span></span><span class="ls124">u<span class="ff1 ls54 ws9a">= 0<span class="_3e blank"> </span></span><span class="ls125">v<span class="ff1 ls54 ws9a">= 0</span></span></span></span></div><div class="t m0 x47 h10 yc7 ff2 fs0 fc0 sc0 ls126">u<span class="ff1 ls127">+</span><span class="ls54 ws9b">\u0131v <span class="ff1 ls128">=</span><span class="ls129">w<span class="ff1 ls128">=</span><span class="ls3">z<span class="ff3 fs1 ls12a v5">2</span><span class="ff1 ls128">=</span><span class="ls8d">x<span class="ff3 fs1 ls12b v5">2</span><span class="ff4 ls12c">\u2212</span><span class="ls91">y<span class="ff3 fs1 ls12b v5">2</span></span></span></span></span><span class="ff1 ws9c">+ 2</span><span class="ws46">xy \u0131<span class="_40 blank"> </span>u<span class="_a blank"> </span><span class="ff1 ls128">=</span><span class="ls8d">x<span class="ff3 fs1 ls12b v5">2</span><span class="ff4 ls12d">\u2212</span><span class="ls8e">y<span class="ff3 fs1 ls12e v5">2</span><span class="ls12f">v</span></span></span><span class="ff1 ws9d">= 2</span>xy</span></span></div><div class="t m0 x75 h10 yc8 ff2 fs0 fc0 sc0 ls101">u<span class="ff1 ls18">=</span><span class="ls54 ws9e">c x<span class="ff3 fs1 ls130 v5">2</span><span class="ff4 ls131">\u2212</span><span class="ls91">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls13">=</span></span><span class="ws9f">c<span class="_41 blank"> </span>x<span class="_42 blank"> </span>c > <span class="ff1 ls132">0</span>y</span></span></div><div class="t m0 x85 h5 yc9 ff2 fs0 fc0 sc0 ls54 wsa0">c < <span class="ff1 ls133">0</span><span class="ls6f">c</span><span class="ff1 ws0">= 0<span class="_43 blank"> </span></span><span class="ls9d">y<span class="ff1 ls13">=<span class="ff4 ls14">±</span></span></span><span class="ws91">x<span class="_44 blank"> </span>v <span class="ff1 ls18">=</span>d</span></div><div class="t m0 x5d h5 yca ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ws52">xy </span><span class="ls18">=</span><span class="ff2 wsa1">d<span class="_45 blank"> </span>y </span><span class="ls18">=</span><span class="ff2 ws5">d/</span>2<span class="ff2 wsa2">x<span class="_20 blank"> </span>d <span class="ff4 ws8">6</span></span><span class="ws0">= 0<span class="_16 blank"> </span><span class="ff2 ls134">d</span>= 0</span></div><div class="t m0 x86 h5 ycb ff2 fs0 fc0 sc0 ls9a">x<span class="ff1 ls54 ws0">= 0<span class="_18 blank"> </span></span><span class="ls9d">y<span class="ff1 ls54 ws0">= 0<span class="_46 blank"> </span></span><span class="ls135">u<span class="ff4 ls21">\u2207</span><span class="ls101">u<span class="ff1 ls54 ws0">= 2</span><span class="ls8d">x<span class="ff9 ls136">i<span class="ff4 ls137">\u2212<span class="ff1 ls54 ws6">2</span></span></span><span class="ls91">y<span class="ff9 ls54">j</span></span></span></span></span></span></div><div class="t m0 x22 h5 ycc ff2 fs0 fc0 sc0 ls138">v<span class="ff4 ls54 ws8">\u2207</span><span class="ls139">v<span class="ff1 ls54 wsa3">= 2</span><span class="ls91">y<span class="ff9 ls13a">i<span class="ff1 ls54 wsa4">+ 2</span></span><span class="ls8d">x<span class="ff9 ls13b">j<span class="ff4 ls21">\u2207</span></span><span class="ls13c">u<span class="ff4 ls54 wsa5">· \u2207</span></span></span></span>v<span class="ff1 ls54 wsa3">= 4</span><span class="ls54 wsa6">xy <span class="ff4 ls13d">\u2212</span><span class="ff1 ws6">4</span><span class="wsa7">xy <span class="ff1 wsa3">= 0</span></span></span></span></div><div class="t m0 x66 h5 ycd ff2 fs0 fc0 sc0 lsff">u<span class="ff1 ls13">=</span><span class="ls54 ws91">c<span class="_1a blank"> </span>v <span class="ff1 ls13">=</span>d</span></div><div class="t m0 x75 h5 yce ff2 fs0 fc0 sc0 ls13e">u<span class="ff1 ls54 wsa8">= 0<span class="_3b blank"> </span></span><span class="ls13f">v<span class="ff1 ls54 wsa8">= 0<span class="_47 blank"> </span>(0</span><span class="ls1f">,<span class="ff1 ls54">0)</span></span></span></div><div class="t m0 x87 h5 ycf ff2 fs0 fc0 sc0 ls101">u<span class="ff1 ls13">=</span><span class="ls54 wsa9">c<span class="_37 blank"> </span>v <span class="ff1 ls13">=</span><span class="ws68">d<span class="_2a blank"> </span>c<span class="_37 blank"> </span>d<span class="_48 blank"> </span>w <span class="ff1 ls18">=</span><span class="ls140">u<span class="ff1 ls141">+</span></span><span class="ws91">\u0131v <span class="ff1 ws0">= 1</span>/z</span></span></span></div><div class="t m0 x88 h2 yd0 ff2 fs0 fc0 sc0 lsc8">u<span class="ff1 ls2e">+</span><span class="ls54 ws91">\u0131v <span class="ff1 ls13">=</span><span class="lsbe">w<span class="ff1 ls142">=<span class="ls54 v1">1</span></span></span></span></div><div class="t m0 x35 h20 yd1 ff2 fs0 fc0 sc0 ls143">z<span class="ff1 ls144 v1">=</span><span class="ls54 v2">z</span></div><div class="t m0 x13 h20 yd1 ff4 fs0 fc0 sc0 ls54 ws8">|<span class="ff2 ls7">z</span>|<span class="ff3 fs1 ls145 v6">2</span><span class="ff1 ls146 v1">=</span><span class="ff2 v2">x</span></div><div class="t m0 x40 h20 yd1 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls79 v6">2</span><span class="ff1 lse v1">+</span><span class="ls147 v1">\u0131</span><span class="ff4 ls14 v2">\u2212</span><span class="ls54 v2">y</span></span></div><div class="t m0 x7 h20 yd1 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls148 v6">2</span><span class="ff1 ls54 ws6 v1">=<span class="_1c blank"></span><span class="ff4 ls7b">\u21d2<span class="ff2 ls101">u<span class="ff1 ls146">=</span><span class="ls54 v1">x</span></span></span></span></span></div><div class="t m0 x64 h20 yd1 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls149 v6">2</span><span class="ls11a v1">v<span class="ff1 ls14a">=<span class="ff4 ls54 ws8 v1">\u2212<span class="ff2">y</span></span></span></span></span></div><div class="t m0 x89 h19 yd1 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls54 v6">2</span></span></div><div class="t m0 x8a h2 yd2 ff2 fs0 fc0 sc0 ls14b">u<span class="ff1 ls14c">=</span><span class="ls54 wsaa">c<span class="_8 blank"> </span>c <span class="ff4 ls14d">\u2208<span class="ff8 ls14e">R</span></span><span class="v1">x</span></span></div><div class="t m0 x81 h21 yd3 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls14f v6">2</span><span class="ff1 ls14c v1">=</span><span class="ls54 wsab v1">c<span class="_49 blank"> </span>x <span class="ff4 ws8">6<span class="ff1 wsac">= 0<span class="ff2 ws11">, y<span class="_3 blank"> </span></span></span>6<span class="ff1 wsac">= 0</span></span></span></span></div><div class="t m0 x1a h5 yd4 ff2 fs0 fc0 sc0 ls6f">c<span class="ff1 ls54 ws0">= 0<span class="_4a blank"> </span></span><span class="ls9a">x<span class="ff1 ls54 ws0">= 0<span class="_4b blank"> </span></span><span class="ls54 wsad">y<span class="_48 blank"> </span>c <span class="ff4 ws8">6<span class="ff1 ws0">= 0</span></span></span></span></div><div class="t m0 x39 h5 yd5 ff2 fs0 fc0 sc0 ls54">x</div><div class="t m0 x8b h3 yd6 ff2 fs0 fc0 sc0 ls8d">x<span class="ff3 fs1 ls45 v6">2</span><span class="ff1 ls2e">+</span><span class="ls91">y<span class="ff3 fs1 ls150 v6">2</span><span class="ff1 ls18 v1">=</span><span class="ls151 v1">c<span class="ff1 ls54 ws6">=<span class="_1c blank"></span><span class="ff4 ls152">\u21d2<span class="ff2 ls8d">x<span class="ff3 fs1 ls45 v5">2</span><span class="ff1 lse">+</span><span class="ls8e">y<span class="ff3 fs1 ls45 v5">2</span></span></span><span class="ls153">\u2212<span class="ff1 ls54 v1">1</span></span></span></span></span></span></div><div class="t m0 x8c h3 yd6 ff2 fs0 fc0 sc0 ls154">c<span class="ls155 v1">x<span class="ff1 ls54 ws0">= 0<span class="_1b blank"> </span>=<span class="_1c blank"></span><span class="ff4 ls7b">\u21d2<span class="ff1 ls54 ws6">(<span class="ff2 ls8c">x</span></span><span class="ls156">\u2212<span class="ff1 ls54 v1">1</span></span></span></span></span></div><div class="t m0 x8d h3 yd6 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls157">c</span><span class="v1">)</span><span class="ff3 fs1 ls45 v3">2</span><span class="ff4 ls158 v1">\u2212</span><span class="v2">1</span></div><div class="t m0 x7f h3 yd6 ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls159">c<span class="ff3 fs1 ls79 v6">2</span></span><span class="lse v1">+<span class="ff2 ls8e">y<span class="ff3 fs1 ls1c v5">2</span></span></span><span class="ws0 v1">= 0<span class="_1b blank"> </span>=<span class="_1c blank"></span><span class="ff4 ls152">\u21d2<span class="ff1 ls2a">(<span class="ff2 ls8c">x</span></span><span class="ls156">\u2212<span class="ff1 ls54 v1">1</span></span></span></span></div><div class="t m0 x3c h3 yd6 ff1 fs0 fc0 sc0 ls54 ws6">2<span class="ff2 ls157">c</span><span class="v1">)</span><span class="ff3 fs1 ls45 v3">2</span><span class="ls2e v1">+<span class="ff2 ls91">y<span class="ff3 fs1 ls1c v5">2</span><span class="ff1 ls15a">=</span></span></span><span class="v2">1</span></div><div class="t m0 x8e h18 yd6 ff1 fs0 fc0 sc0 ls54 ws6">4<span class="ff2 ls159">c</span><span class="ff3 fs1 v6">2</span></div><div class="t m0 x8f h1b yd7 ff2 fs0 fc0 sc0 ls15b">u<span class="ff1 ls15c">=</span><span class="ls15d">c<span class="ff1 ls15e">(<span class="ff3 fs1 ls54 v5">1</span></span></span></div><div class="t m0 x45 h35 yd8 ff3 fs1 fc0 sc0 ls54 ws3d">2<span class="ff6 ls15f">c<span class="ff2 fs0 ls1f v4">,<span class="ff1 ls54 wsae">0) </span></span></span><span class="v12">1</span></div><div class="t m0 x90 h14 yd8 ff3 fs1 fc0 sc0 ls68">2<span class="ff7 ls160">|<span class="ff6 ls161">c</span><span class="ls162">|<span class="ff1 fs0 ls54 ws6 v4">(0<span class="ff2 ls1f">,</span>0)</span></span></span></div><div class="t m0 x81 h5 yd9 ff1 fs0 fc0 sc0 ls54 ws6">(0<span class="ff2 ls1f">,</span><span class="wsaf">0) <span class="ff2">x</span></span></div><div class="t m0 x91 h5 yda ff2 fs0 fc0 sc0 ls54 wsb0">c c</div><div class="t m0 x71 h5 ydb ff2 fs0 fc0 sc0 ls11a">v<span class="ff1 ls13">=</span><span class="ls54 wsb1">d d<span class="_4c blank"> </span>y</span></div><div class="t m0 x74 h5 ydc ff2 fs0 fc0 sc0 ls54 wsb2">f<span class="_4d blank"> </span>D<span class="_46 blank"> </span>z <span class="ff1 wsb3">= 0<span class="_4e blank"> </span></span><span class="lsa7">f<span class="ff1 ls2a">(</span><span class="ls7">z</span></span><span class="ff1 wsb3">) = </span><span class="ws5">u<span class="ff1 ws6">(</span><span class="wsb4">r<span class="_15 blank"></span>,<span class="_4f blank"> </span>\u03b8 <span class="ff1 wsb5">) +</span></span></span></div><div class="t m0 x1a h5 ydd ff2 fs0 fc0 sc0 ls54 wsb6">\u0131v <span class="ff1 ws6">(</span><span class="wsb4">r<span class="_15 blank"></span>,<span class="_4f blank"> </span>\u03b8 <span class="ff1 ls163">)</span><span class="wsb7">D u</span></span></div><div class="t m0 x92 h5 yde ff2 fs0 fc0 sc0 ls54">v</div><div class="t m0 x84 h23 ydf ff2 fs0 fc0 sc0 lsf5">r<span class="ff3 fs1 ls84 v5">2</span><span class="ls164 v1">\u2202</span><span class="ff3 fs1 ls2f v10">2</span><span class="ls54 v1">u</span></div><div class="t m0 x1f h20 ye0 ff2 fs0 fc0 sc0 ls54 wsb8">\u2202<span class="_2c blank"> </span>r <span class="ff3 fs1 ls165 v6">2</span><span class="ff1 ls2e v1">+</span><span class="ls166 v1">r</span><span class="ws6c v2">\u2202 u</span></div><div class="t m0 x93 h33 ye0 ff2 fs0 fc0 sc0 ls54 ws6c">\u2202 r<span class="_3 blank"> </span><span class="ff1 ls50 v1">+</span><span class="ls167 v2">\u2202</span><span class="ff3 fs1 ls38 v21">2</span><span class="v2">u</span></div><div class="t m0 x20 h21 ye0 ff2 fs0 fc0 sc0 ls54 wsb9">\u2202<span class="_2c blank"> </span>\u03b8 <span class="ff3 fs1 ls168 v6">2</span><span class="ff1 ws0 v1">= 0</span></div><div class="t m0 x94 h5 ye1 ff2 fs0 fc0 sc0 ls54 ws8e">u v</div><div class="t m0 x95 hb ye2 ff2 fs0 fc0 sc0 lsd6">u<span class="ff6 fs1 ls169 va">r</span><span class="ff1 ls16a">=</span><span class="lse4">r<span class="ff7 fs1 ls54 ws13 v5">\u2212<span class="ff3 ls2f">1</span></span><span class="lsd3">v<span class="ff6 fs1 ls16b va">\u03b8</span><span class="ls54 ws5">u<span class="ff6 fs1 ls16c va">\u03b8</span><span class="ff1 ls16d">=</span><span class="ff4 ws8">\u2212</span><span class="ws24">r v<span class="ff6 fs1 va">r</span></span></span></span></span></div><div class="t m0 x10 h23 ye3 ff2 fs0 fc0 sc0 lse4">r<span class="ff3 fs1 ls84 v5">2</span><span class="ls164 v1">\u2202</span><span class="ff3 fs1 ls2f v10">2</span><span class="ls54 v1">u</span></div><div class="t m0 x96 h3 ye4 ff2 fs0 fc0 sc0 ls54 wsba">\u2202<span class="_2c blank"> </span>r <span class="ff3 fs1 ls16e v6">2</span><span class="ff1 ls2e v1">+</span><span class="ls166 v1">r</span><span class="ws6c v2">\u2202 u</span></div><div class="t m0 x3b h4 ye4 ff2 fs0 fc0 sc0 ls54 ws6c">\u2202 r<span class="_3 blank"> </span><span class="ff1 ls50 v1">+</span><span class="ls164 v2">\u2202</span><span class="ff3 fs1 ls2f v21">2</span><span class="v2">u</span></div><div class="t m0 x78 h30 ye4 ff2 fs0 fc0 sc0 ls54 wsb9">\u2202<span class="_2c blank"> </span>\u03b8 <span class="ff3 fs1 ls168 v6">2</span><span class="ff1 ls18 v1">=</span><span class="lsf5 v1">r</span><span class="ff3 fs1 ls2f v3">2</span><span class="ls16f v1">\u2202</span><span class="ff6 fs1 ls170 v1e">r</span><span class="ff1 ws6 v1">(</span><span class="ws5 v1">u</span><span class="ff6 fs1 ls170 v1e">r</span><span class="ff1 ws1 v1">) + </span><span class="ws24 v1">r u</span><span class="ff6 fs1 ls171 v1e">r</span><span class="ff1 ls2e v1">+</span><span class="ls16f v1">\u2202</span><span class="ff6 fs1 ls172 v1e">\u03b8</span><span class="ff1 ls2a v1">(</span><span class="ws5 v1">u</span><span class="ff6 fs1 ls173 v1e">\u03b8</span><span class="ff1 v1">)</span></div><div class="t m0 x44 hb ye5 ff1 fs0 fc0 sc0 ls18">=<span class="ff2 lsf5">r<span class="ff3 fs1 ls2f v5">2</span><span class="ls16f">\u2202<span class="ff6 fs1 ls170 va">r</span></span></span><span class="ls54 ws6">(<span class="ff2 lsf5">r<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls2f">1</span></span><span class="ls54 ws5">v<span class="ff6 fs1 ls173 va">\u03b8</span></span></span><span class="ws1">) + <span class="ff2 ws24">r r <span class="ff7 fs1 ws13 v5">\u2212<span class="ff3 ls2f">1</span></span><span class="lsd3">v<span class="ff6 fs1 ls174 va">\u03b8</span></span></span><span class="ls2e">+<span class="ff2 ls16f">\u2202<span class="ff6 fs1 ls173 va">\u03b8</span></span></span></span>(<span class="ff4 ls14">\u2212</span><span class="ff2 ws24">r v<span class="ff6 fs1 ls170 va">r</span></span>)</span></div><div class="t m0 x44 hb ye6 ff1 fs0 fc0 sc0 ls18">=<span class="ff4 ls54 ws8">\u2212<span class="ff2 lsf5">r<span class="ff3 fs1 ls38 v5">2</span>r<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls2f">2</span></span><span class="ls54 ws5">v<span class="ff6 fs1 ls175 va">\u03b8</span></span></span></span><span class="ls2e">+<span class="ff2 lse4">r<span class="ff3 fs1 ls2f v5">2</span><span class="lsf5">r<span class="ff7 fs1 ls29 v5">\u2212<span class="ff3 ls2f">1</span></span><span class="lsd3">v<span class="ff6 fs1 ls54 wsbb va">\u03b8r<span class="_a blank"> </span></span></span></span></span>+<span class="ff2 ls54 ws5">v<span class="ff6 fs1 ls175 va">\u03b8</span><span class="ff4 lsb">\u2212</span><span class="ws24">rv<span class="ff6 fs1 wsbb va">r \u03b8</span></span></span></span></div><div class="t m0 x44 h5 ye7 ff1 fs0 fc0 sc0 ls18">=<span class="ff4 ls54 ws8">\u2212<span class="ff2 ws5">v<span class="ff6 fs1 ls175 va">\u03b8</span></span></span><span class="ls2e">+<span class="ff2 ls54 ws24">r v<span class="ff6 fs1 wsbb va">\u03b8r<span class="_a blank"> </span></span></span>+<span class="ff2 lsd3">v<span class="ff6 fs1 ls174 va">\u03b8</span><span class="ff4 lsb">\u2212</span><span class="ls54 ws24">rv<span class="ff6 fs1 wsbb va">r \u03b8<span class="_50 blank"> </span></span></span></span><span class="ls54 ws0">= 0</span></span></div><div class="t m0 x8b h5 ye8 ff2 fs0 fc0 sc0 lsd3">v<span class="ff6 fs1 ls54 wsbb va">r\u03b8<span class="_50 blank"> </span></span><span class="ff1 ls13">=</span>v<span class="ff6 fs1 ls54 wsbb va">\u03b8 r<span class="_51 blank"> </span></span><span class="ls54">v</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w3 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg8.png"><div class="t m0 x2d h5 y29 ff2 fs0 fc0 sc0 ls176">u<span class="ff1 ls54 wsbc">= ln(</span><span class="lse4">r<span class="ff1 ls177">)</span><span class="ls54 wsbd">r<span class="_52 blank"> </span>> <span class="ff1 wsbe">0<span class="_53 blank"> </span>0 </span><span class="wsbf">< \u03b8<span class="_52 blank"> </span>< <span class="ff1 ws6">2</span>\u03c0</span></span></span></div><div class="t m0 x97 h5 ye9 ff2 fs0 fc0 sc0 ls54">u</div><div class="t m0 x98 h5 yea ff2 fs0 fc0 sc0 ls54">v</div><div class="t m0 x99 h12 yeb ff2 fs0 fc0 sc0 lsd6">u<span class="ff6 fs1 ls178 va">r</span><span class="ff1 ls1b">=<span class="ls54 v1">1</span></span></div><div class="t m0 x6f h2f yec ff2 fs0 fc0 sc0 ls179">r<span class="ls54 ws5 v1">v</span><span class="ff6 fs1 ls17a v1e">\u03b8</span><span class="ls54 ws5 v1">u</span><span class="ff6 fs1 ls17b v1e">\u03b8</span><span class="ff1 ls13 v1">=<span class="ff4 ls14">\u2212<span class="ff2 ls54 ws24">r v<span class="ff6 fs1 va">r</span></span></span></span></div><div class="t m0 x73 h2 yed ff2 fs0 fc0 sc0 ls54 ws5">v<span class="ff6 fs1 ls17c va">r</span><span class="ff1 ls13">=<span class="ff4 lsf8">\u2212</span><span class="ls54 v1">1</span></span></div><div class="t m0 x35 h20 yee ff2 fs0 fc0 sc0 ls17d">r<span class="ls54 ws5 v1">u</span><span class="ff6 fs1 ls17b v1e">\u03b8</span><span class="ff1 ls54 ws0 v1">= 0<span class="_54 blank"> </span></span><span class="lsd6 v1">u</span><span class="ff6 fs1 ls17b v1e">\u03b8</span><span class="ff1 ls54 ws0 v1">= 0;<span class="_b blank"> </span></span><span class="ls54 ws5 v1">v</span><span class="ff6 fs1 ls17b v1e">\u03b8</span><span class="ff1 ls54 wsc0 v1">== </span><span class="ls54 ws24 v1">r u</span><span class="ff6 fs1 ls178 v1e">r</span><span class="ff1 ls54 ws0 v1">= 1<span class="_54 blank"> </span></span><span class="ls54 ws5 v1">u</span><span class="ff6 fs1 ls17c v1e">r</span><span class="ff1 ls1b v1">=<span class="ls54 v1">1</span></span></div><div class="t m0 x3c h2f yee ff2 fs0 fc0 sc0 ls179">r<span class="ls54 v1">.</span></div><div class="t m0 x60 h5 yef ff2 fs0 fc0 sc0 lsd3">v<span class="ff6 fs1 ls17e va">r</span><span class="ff1 ls54 wsc1">= 0<span class="_29 blank"> </span></span><span class="ls54 wsc2">v<span class="_55 blank"> </span>r<span class="_56 blank"> </span>v <span class="ff1 ws6">(</span><span class="wsb4">r<span class="_15 blank"></span>,<span class="_4f blank"> </span>\u03b8 <span class="ff1 wsc1">) = </span><span class="ws5">h<span class="ff1 ls2a">(</span><span class="ls48">\u03b8<span class="ff1 ls17f">)</span></span>h</span></span></span></div><div class="t m0 x25 hb yf0 ff2 fs0 fc0 sc0 ls54 wsc3">\u03b8 v<span class="ff6 fs1 ls180 va">\u03b8</span><span class="ff1 wsc4">= 1<span class="_33 blank"> </span></span><span class="ws5">h<span class="ff7 fs1 lsa6 v5">0</span><span class="ff1 ls2a">(</span><span class="ls48">\u03b8<span class="ff1 ls181 wsc5">)=1 </span></span>h<span class="ff1 ls2a">(</span><span class="ls48">\u03b8</span><span class="ff1 wsc6">) = </span><span class="ls182">\u03b8<span class="ff1 ls183">+</span></span><span class="wsc7">c<span class="_57 blank"> </span>c <span class="ff4 ls184">\u2208</span><span class="ff8">R</span></span></span></div><div class="t m0 x38 h5 yf1 ff2 fs0 fc0 sc0 ls54 wsc2">u<span class="_58 blank"> </span>v <span class="ff1 ws6">(</span><span class="wsb4">r<span class="_15 blank"></span>,<span class="_4f blank"> </span>\u03b8 <span class="ff1 ws4e">) = </span><span class="lsd">\u03b8<span class="ff1 ls2e">+</span></span>c</span></div><div class="t m0 xe h1a yf2 ff1 fs0 fc0 sc0 ls54 wsc8">exp(0)<span class="_4 blank"> </span>=<span class="_4 blank"> </span>1<span class="_7 blank"> </span>exp(2 <span class="ff4 ls27">±</span><span class="ws6">3<span class="ff2 ws46">\u03c0 \u0131</span><span class="ws67">) = <span class="ff4 ls185">\u2212</span><span class="lsf2">e<span class="ff3 fs1 ls186 v5">2</span></span><span class="wsc9">exp( <span class="ff6 fs1 v5">\u03c0</span></span></span></span></div><div class="t m0 x9a h36 yf3 ff3 fs1 fc0 sc0 ls187">2<span class="ff2 fs0 ls54 ws5 v4">\u0131<span class="ff1 ws67">) = <span class="ff2 ls188">\u0131</span><span class="wsc9">exp( </span></span></span><span class="ls54 ws3d v12">2+<span class="ff6 wsca">\u03c0 \u0131</span></span></div><div class="t m0 x9b h37 yf3 ff3 fs1 fc0 sc0 ls189">4<span class="ff1 fs0 ls54 ws67 v4">) = <span class="ff5 ls18a v23">q</span></span><span class="ls54 v12">e</span></div><div class="t m0 x9c h16 yf3 ff3 fs1 fc0 sc0 ls18b">2<span class="ff1 fs0 ls54 ws1 v4">(1 + <span class="ff2 ws5">\u0131<span class="ff1">)</span></span></span></div><div class="t m0 x73 hb yf4 ff1 fs0 fc0 sc0 ls54 ws6">exp(<span class="ff2 ls7">z</span><span class="ws0">) = exp(<span class="ff2 ls8c">x</span><span class="ls2e">+</span><span class="ff2 ws70">\u0131y </span>) =<span class="_1d blank"> </span>e<span class="ff6 fs1 lsbf v5">x</span><span class="ff4 ws8">{</span></span>cos(<span class="ff2 ls8e">y</span><span class="ws1">) + <span class="ff2 ls52">\u0131</span></span>sen(<span class="ff2 ls8e">y</span><span class="ls2a">)</span><span class="ff4">}</span></div><div class="t m0 x1a h1a yf5 ff1 fs0 fc0 sc0 ls54 wsc9">exp( <span class="ff3 fs1 ws3d v5">2+<span class="ff6 wsca">\u03c0 \u0131</span></span></div><div class="t m0 x92 h35 yf6 ff3 fs1 fc0 sc0 ls189">4<span class="ff1 fs0 ls54 ws0 v4">) = exp(<span class="_59 blank"> </span></span><span class="ls54 v12">1</span></div><div class="t m0 x9d h36 yf6 ff3 fs1 fc0 sc0 ls18c">2<span class="ff1 fs0 ls18d v4">+<span class="ff2 ls58">\u0131</span></span><span class="ff6 ls54 v12">\u03c0</span></div><div class="t m0 x9e h38 yf6 ff3 fs1 fc0 sc0 ls187">4<span class="ff1 fs0 ls54 ws0 v4">) =<span class="_1d blank"> </span>e</span><span class="ls54 ws3d v13">1<span class="ff6 ws20">/<span class="ff3 ls38">2</span><span class="ff4 fs0 ws8 v20">{<span class="ff1 ws6">cos(<span class="ff2 ws46">\u03c0 /</span><span class="wscb">4) + <span class="ff2 ls31">\u0131</span></span>sen(<span class="ff2 ws46">\u03c0 /</span>4)<span class="ff4 lsf3">}</span><span class="ws86">= e</span></span></span></span>1<span class="ff6 ws20">/</span><span class="ls38">2<span class="ff4 fs0 ls18e v20">{</span><span class="ff7 lsc2 v1e">\u221a</span></span><span class="v0">2</span></span></div><div class="t m0 x6e h38 yf6 ff3 fs1 fc0 sc0 ls18f">2<span class="ff1 fs0 ls18d v4">+<span class="ff2 ls190">\u0131</span></span><span class="ff7 lsc2 v24">\u221a</span><span class="ls54 v12">2</span></div><div class="t m0 x9f h39 yf6 ff3 fs1 fc0 sc0 ls191">2<span class="ff4 fs0 ls192 v4">}<span class="ff1 ls13">=<span class="ff4 ls193 v13">\u221a</span><span class="ls194">e</span></span></span><span class="ff7 lsc2 v24">\u221a</span><span class="ls54 v12">2</span></div><div class="t m0 xa0 h39 yf6 ff3 fs1 fc0 sc0 ls191">2<span class="ff4 fs0 ls55 v4">{<span class="ff1 ls54 wscb">1 + <span class="ff2 ws5">\u0131<span class="ff4 lsf3">}</span></span><span class="ls13">=<span class="ff4 ls195 v13">\u221a</span><span class="ls196">e</span></span></span></span><span class="ls54 v12">1</span></div><div class="t m0 xa1 h3a yf7 ff7 fs1 fc0 sc0 lsc2">\u221a<span class="ff3 ls51 v25">2</span><span class="ff4 fs0 ls55 va">{<span class="ff1 ls54 wscb">1 + <span class="ff2 ws5">\u0131<span class="ff4">}</span></span></span></span></div><div class="t m0 xe h2 yf8 ff1 fs0 fc0 sc0 ls54 ws6">exp(<span class="ff2 lsa">z</span><span class="ls2e">+</span><span class="ff2 ws46">\u03c0 \u0131</span><span class="ws67">) = <span class="ff4 ls185">\u2212</span></span>exp(<span class="ff2 ls7">z</span><span class="wscc">) exp(<span class="ff4 ws8">\u2212<span class="ff2 wscd">nz </span></span><span class="ws0">) =<span class="_b blank"> </span><span class="v1">1</span></span></span></div><div class="t m0 x38 h2f yf9 ff1 fs0 fc0 sc0 ls54 ws6">(exp(<span class="ff2 ls3">z</span>))<span class="ff6 fs1 ls197 v6">n</span><span class="ff2 wsce v1">,<span class="_1d blank"> </span>n </span><span class="ws0 v1">= 1<span class="ff2 ls3a">,</span></span><span class="v1">2<span class="ff2 ls198 wscf">,....<span class="_1c blank"></span></span></span></div><div class="t m0 xa2 h5 yfa ff2 fs0 fc0 sc0 ls54 ws19">z<span class="_5a blank"> </span>z <span class="ff1 ls13">=</span><span class="lse1">r</span><span class="ff1 ws6">exp(</span><span class="wsd0">\u0131\u03b8 <span class="ff1">)</span></span></div><div class="t m0 xe h5 yfb ff2 fs0 fc0 sc0 ls1a">z<span class="ff1 ls13">=</span><span class="lse1">r<span class="ff1 ls54 ws6">exp(<span class="ff4 ws8">\u2212</span></span><span class="ls54 wsd1">\u0131\u03b8 <span class="ff1 wscc">) exp(ln(</span><span class="lse4">r</span><span class="ff1 ws1">) + </span><span class="wsd0">\u0131\u03b8 <span class="ff1 ws4e">) = </span>z</span></span></span></div><div class="t m0 xa3 h5 yfc ff2 fs0 fc0 sc0 ls54">z</div><div class="t m0 xe h1f yfd ff1 fs0 fc0 sc0 ls54 ws6">exp(<span class="ff2 ls7">z</span><span class="ws4e">) = <span class="ff4 ls14">\u2212</span><span class="wsd2">2 exp(<span class="ff2 ls7">z</span><span class="ws0">) = 1<span class="_6 blank"> </span>+<span class="_6 blank"> </span><span class="ff2 ws5">\u0131<span class="ff4 ls21 v9">\u221a</span></span><span class="wsd3">3 exp(2<span class="ff2 ls11">z<span class="ff4 lsb">\u2212</span></span><span class="ws47">1) = 1</span></span></span></span></span></div><div class="t m0 x12 h5 yfe ff1 fs0 fc0 sc0 ls54 ws6">exp(<span class="ff2 wsd4">\u0131z </span><span class="ls88">)</span><span class="ff4 ws8">6</span><span class="wsd5">= exp(<span class="ff2 ws18">\u0131z </span><span class="ls199">)<span class="ff2 ls23">z</span><span class="ls18">=</span></span><span class="ff4 ws8">±<span class="ff2 ws1d">n\u03c0<span class="_40 blank"> </span>n </span></span><span class="ws0">= 0<span class="ff2 ls1f">,</span></span></span>1<span class="ff2 ls1f">,</span>2<span class="ff2 ws11">, . . .</span></div><div class="t m0 x12 h10 yff ff4 fs0 fc0 sc0 lsc">|<span class="ff1 ls54 ws6">exp(2<span class="ff2 lsa">z</span><span class="lse">+</span><span class="ff2 ws5">\u0131</span>)</span><span class="ls54 wsd6">|<span class="_5b blank"> </span>| <span class="ff1 ws6">exp(<span class="ff2 ws18">\u0131z <span class="ff3 fs1 ls2f v5">2</span></span>)</span>|</span></div><div class="t m0 x28 h1e y100 ff4 fs0 fc0 sc0 ls19a">|<span class="ff1 ls54 ws6">exp(2<span class="ff2 lsa">z</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131</span><span class="ws1">) + exp(<span class="ff2 wsd4">\u0131z <span class="ff3 fs1 ls38 v5">2</span></span></span>)</span><span class="ls54 ws53">| \u2264<span class="_1d blank"> </span><span class="ff1 ws6">e<span class="ff3 fs1 ws3d v5">2<span class="ff6 lsd7">x</span></span><span class="ws25">+ e<span class="ff7 fs1 ws13 v5">\u2212<span class="ff3 ws3d">2<span class="ff6">xy</span></span></span></span></span></span></div><div class="t m0 x77 h5 y101 ff1 fs0 fc0 sc0 ls54 ws6">exp(<span class="ff2 ls8c">x</span><span class="ls2e">+</span><span class="ff2 ws70">\u0131y </span><span class="ls19b">)<span class="ff2 ls9a">x</span></span><span class="ff4 ws53">\u2192 \u221e<span class="_5c blank"> </span></span><span class="ws1">exp(2 + <span class="ff2 ws70">\u0131y </span><span class="ls19c">)<span class="ff2 lsb4">y</span></span><span class="ff4 ws53">\u2192 \u221e</span></span></div><div class="t m0 x74 hb y102 ff4 fs0 fc0 sc0 ls19a">|<span class="ff1 ls54 ws6">exp(<span class="ff2 ls8c">x</span><span class="lse">+</span><span class="ff2 ws4f">\u0131y </span>)</span><span class="ls17">|<span class="ff1 ls54 ws86">= e<span class="ff6 fs1 lsd2 v5">x</span></span><span class="ls54 ws53">\u2192 \u221e<span class="_5d blank"> </span><span class="ff2 ls9a">x</span><span class="wsd7">\u2192<span class="_4 blank"> </span>\u221e<span class="_1a blank"> </span>| <span class="ff1 ws1">exp(2 + <span class="ff2 ws4f">\u0131y </span><span class="ls2a">)</span></span><span class="ls89">|</span><span class="ff1 ws86">= e<span class="ff3 fs1 ls1c v5">2</span></span><span class="ls19d">\u2192</span><span class="ff1 ws6">e<span class="ff3 fs1 ls19e v5">2</span><span class="ff2 ls9d">y</span></span></span>\u2192 \u221e</span></span></div><div class="t m0 x4a hb y103 ff2 fs0 fc0 sc0 lsbe">w<span class="ff1 ls54 ws0">= 2</span><span class="ls3">z<span class="ff3 fs1 ls45 v5">2</span><span class="ff4 lsb">\u2212<span class="ff1 ls15">3</span>\u2212</span><span class="lse0">z<span class="ff1 lsf2">e<span class="ff6 fs1 ls19f v5">z</span><span class="ls54 ws25">+ e<span class="ff7 fs1 ws13 v5">\u2212<span class="ff6">z</span></span></span></span></span></span></div><div class="t m0 xa4 hf y104 ff2 fs0 fc0 sc0 ls54 wsd8">w<span class="_5e blank"> </span>w <span class="ff1 wsd9">= 2</span><span class="ls7">z<span class="ff3 fs1 ls1a0 v5">3</span><span class="ff4 ls1a1">\u2212</span></span><span class="ff1">3</span></div><div class="t m0 x1a hb y105 ff2 fs0 fc0 sc0 lsbe">w<span class="ff1 ls13">=<span class="ff4 ls14">\u2212</span></span><span class="lse0">z<span class="ff1 lsf2">e<span class="ff6 fs1 ls1a2 v5">z</span></span><span class="ls6b">w<span class="ff1 ls54 ws86">= e<span class="ff7 fs1 ws13 v5">\u2212<span class="ff6">z</span></span></span></span></span></div><div class="t m0 x12 h5 y106 ff2 fs0 fc0 sc0 lsbe">w<span class="ff1 ls54 ws0">= exp(</span><span class="ls7">z<span class="ff1 ls54">)</span></span></div><div class="t m0 x2f h10 y107 ff2 fs0 fc0 sc0 ls6b">w<span class="ff1 ls54 ws0">= exp(</span><span class="ls3">z<span class="ff3 fs1 ls2f v5">2</span><span class="ff1 ls54">)</span></span></div><div class="t m0 x12 h5 y4b ff1 fs0 fc0 sc0 ls54 ws6">Re(exp(1<span class="ff2 ws49">/z </span><span class="wsda">)) <span class="ff2 wsdb">x y</span></span></div><div class="t m0 x1b h5 ye8 ff2 fs0 fc0 sc0 ls1a">z<span class="ff1 ls54 ws0">= 0</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w4 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bg9.png"><div class="t m0 x30 h5 y29 ff4 fs0 fc0 sc0 lsc">|<span class="ff1 ls54 ws6">senh(<span class="ff2 ls8e">y</span>)</span><span class="lsc6 wsdc">|\u2264|<span class="_5f blank"></span><span class="ff1 ls54 ws6">sen(<span class="ff2 ls7">z</span>)<span class="ff4 wsdd">| \u2264 </span>cosh(<span class="ff2 ls91">y</span><span class="ls1a3">)<span class="ff4 lsc">|</span></span>senh(<span class="ff2 ls8e">y</span><span class="ls2a">)</span><span class="ff4 wsde">|<span class="_4 blank"> </span>\u2264<span class="_4 blank"> </span>| </span>cos(<span class="ff2 ls3">z</span>)<span class="ff4 wsdf">| \u2264 </span>cosh(<span class="ff2 ls91">y</span>)</span></span></div><div class="t m0 x1a h5 y2a ff2 fs0 fc0 sc0 ls1a">z<span class="ff1 ls13">=</span><span class="ls8c">x<span class="ff1 ls2e">+</span><span class="ls54">\u0131y</span></span></div><div class="t m0 x62 h5 y108 ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 wsd4">\u0131z </span><span class="wse0">) = cos(<span class="ff2 wsd4">\u0131z </span><span class="ls1a4">)<span class="ff2 ls1a5">z</span></span></span>sen(<span class="ff2 ws18">\u0131z </span><span class="ls1a6">)</span><span class="ff4 ws8">6</span><span class="wse1">= sen(<span class="ff2 wsd4">\u0131z </span><span class="ls1a7">)<span class="ff2 ls1a8">z</span><span class="ls1a9">=</span></span><span class="ff4 ws8">±<span class="ff2 ws46">n\u03c0 \u0131</span></span></span></div><div class="t m0 x1a h5 y109 ff2 fs0 fc0 sc0 ls1e">n<span class="ff1 ls54 ws0">= 0</span><span class="ls3a">,<span class="ff1 ls54 ws6">1</span><span class="ls1f">,<span class="ff1 ls54 ws6">2</span><span class="ls54 ws11">, . . .</span></span></span></div><div class="t m0 x82 h5 y10a ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ws18">\u0131z </span><span class="ws47">) = cos(<span class="ff2 lsba">y</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131x</span><span class="ws0">) = cos(<span class="ff2 ls91">y</span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ls39">)<span class="ff4 ls27">\u2212<span class="ff2 ls52">\u0131</span></span></span></span></span></span>sen(<span class="ff2 ls8e">y</span><span class="ws23">) senh(<span class="ff2 ls8d">x</span>)</span></div><div class="t m0 x1a h5 y10b ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 wsd4">\u0131z </span><span class="ws4e">) = cos(<span class="ff4 ls14">\u2212<span class="ff2 lsba">y</span></span><span class="ls2e">+</span><span class="ff2 ws5">\u0131x</span>) = cos(<span class="ff4 ls14">\u2212<span class="ff2 ls91">y</span></span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ls39">)<span class="ff4 lsb">\u2212<span class="ff2 ls31">\u0131</span></span></span></span></span>sen(<span class="ff4 ls14">\u2212<span class="ff2 ls91">y</span></span><span class="ws23">) senh(<span class="ff2 ls8d">x</span><span class="ws0">) = cos(<span class="ff2 ls91">y</span></span>) cosh(<span class="ff2 ls8f">x</span></span>)<span class="ff4 ws8">\u2212<span class="ff2 ls31">\u0131</span></span>sen(<span class="ff2 ls91">y</span><span class="ws23">) senh(<span class="ff2 ls8d">x</span><span class="ws47">) = cos(<span class="ff2 ws18">\u0131z </span>)</span></span></div><div class="t m0 x70 h5 y10c ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ws18">\u0131z </span><span class="ws0">) =<span class="_1d blank"> </span>sen(<span class="ff2 lsba">y</span><span class="ls2e">+</span><span class="ff2 ws5">\u0131x</span>) =<span class="_1d blank"> </span>sen(<span class="ff2 ls91">y</span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ws1">) + <span class="ff2 ls52">\u0131</span></span></span></span>cos(<span class="ff2 ls8e">y</span><span class="ws23">) senh(<span class="ff2 ls8d">x</span>)</span></div><div class="t m0 x7e h5 y10d ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 wsd4">\u0131z </span><span class="ws0">) =<span class="_1d blank"> </span>sen(<span class="ff4 ls14">\u2212<span class="ff2 lsba">y</span></span><span class="ls2e">+</span><span class="ff2 ws5">\u0131x</span>) =<span class="_1d blank"> </span>sen(<span class="ff4 ls14">\u2212<span class="ff2 ls8e">y</span></span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ws1">) + <span class="ff2 ls31">\u0131</span></span></span></span>cos(<span class="ff4 ws8">\u2212<span class="ff2 ls91">y</span></span><span class="ws23">) senh(<span class="ff2 ls8d">x</span><span class="ws4e">) = <span class="ff4 ls185">\u2212</span></span></span>sen(<span class="ff2 ls91">y</span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ls39">)<span class="ff4 ls27">\u2212<span class="ff2 ls52">\u0131</span></span></span></span>cos(<span class="ff2 ls91">y</span><span class="ws23">) senh(<span class="ff2 ls8d">x</span>)</span></div><div class="t m0 x7a h5 y10e ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ws18">\u0131z </span><span class="ws0">) =<span class="_1d blank"> </span>sen(<span class="ff2 wsd4">\u0131z </span>)</span></div><div class="t m0 x3f h5 y10f ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls91">y</span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ws67">) = <span class="ff4 ls185">\u2212</span></span></span>sen(<span class="ff2 ls91">y</span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="wse2">) cos(<span class="ff2 ls91">y</span></span>) senh(<span class="ff2 ls8d">x</span><span class="ws67">) = <span class="ff4 ls185">\u2212</span></span></span>cos(<span class="ff2 ls8e">y</span><span class="ws23">) senh(<span class="ff2 ls8d">x</span>)</span></div><div class="t m0 x13 h5 y110 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls8e">y</span><span class="ws23">) cosh(<span class="ff2 ls8d">x</span><span class="ws47">) = 0<span class="_60 blank"> </span>cos(<span class="ff2 ls91">y</span></span>) senh(<span class="ff2 ls8d">x</span><span class="ws47">) = 0</span></span></div><div class="t m0 xa5 h5 y111 ff1 fs0 fc0 sc0 ls54 ws6">cosh(<span class="ff2 ls8d">x</span><span class="ls1aa">)</span><span class="ff4 ws8">6</span><span class="ws0">= 0<span class="_61 blank"> </span><span class="ff2 ls9a">x<span class="ff4 ls34">\u2208<span class="ff8 ls1ab">R</span></span></span></span>sen(<span class="ff2 ls91">y</span><span class="ws47">) = 0<span class="_62 blank"> </span>cos(<span class="ff2 ls91">y</span><span class="ls88">)</span><span class="ff4 ws8">6</span><span class="ws0">= 0</span></span></div><div class="t m0 x1a h5 y112 ff1 fs0 fc0 sc0 ls54 ws6">senh(<span class="ff2 ls8f">x</span><span class="ws47">) = 0<span class="_42 blank"> </span><span class="ff2 ls9a">x</span><span class="ws0">= 0<span class="_4b blank"> </span><span class="ff2 ls9d">y</span><span class="ls13">=</span><span class="ff2 wse3">k \u03c0<span class="_9 blank"> </span>k<span class="_16 blank"> </span>x<span class="_4 blank"> </span></span>= 0<span class="_63 blank"> </span><span class="ff2 ls23">z</span><span class="ls18">=<span class="ff2 ls1ac">x</span><span class="ls1ad">+</span></span><span class="ff2 wse4">\u0131y </span><span class="wse5">=<span class="_4 blank"> </span>0 + <span class="ff2 wse3">k \u03c0 \u0131<span class="_4 blank"> </span></span><span class="ls18">=</span><span class="ff2 wse3">k \u03c0 \u0131</span></span></span></span></div><div class="t m0 x5a h5 y113 ff2 fs0 fc0 sc0 ls54">k</div><div class="t m0 xe h5 y114 ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="ws47">) = cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">2</span></span><span class="ls1ae">)</span><span class="ff2 ws5">z<span class="ff3 fs1 ls1c va">2</span></span><span class="ls18">=</span><span class="ff4 ws8">±<span class="ff2 ws5">z<span class="ff3 fs1 ls45 va">1</span></span><span class="lsb">±</span></span></span>2<span class="ff2 ws1d">n\u03c0<span class="_11 blank"> </span>n </span><span class="ws0">= 0<span class="ff2 ls1f">,</span></span>1<span class="ff2 ls3a">,</span>2<span class="ff2 ws11">, . . .</span></div><div class="t m0 x55 h5 y115 ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ls1af">A</span><span class="ls1b0">+<span class="ff2 ls1b1">B</span></span><span class="wse6">) = cos(<span class="ff2 ws5">A</span><span class="ws23">) cos(<span class="ff2 ls5e">B</span><span class="ls1b2">)<span class="ff4 ls1b3">\u2212</span></span></span></span>sen(<span class="ff2 ls1b4">A</span><span class="ws23">) sen(<span class="ff2 ls1b1">B</span>)</span></div><div class="t m0 x16 h5 y116 ff2 fs0 fc0 sc0 ls54 wse7">A B</div><div class="t m0 xa6 h5 y117 ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="ls39">)<span class="ff4 lsb">\u2212</span></span>cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls38 va">2</span></span><span class="ws47">) = cos(<span class="ff2 ls5d">A<span class="ff4 lsb">\u2212</span><span class="ls5e">B</span></span><span class="ls39">)<span class="ff4 lsb">\u2212</span></span></span>cos(<span class="ff2 ls5d">A</span><span class="ls2e">+<span class="ff2 ls5e">B</span></span><span class="ws0">) = 2<span class="_4f blank"> </span>sen(<span class="ff2 ws5">A</span><span class="ws23">) sen(<span class="ff2 ls5e">B</span>)</span></span></div><div class="t m0 xa7 h5 y118 ff2 fs0 fc0 sc0 ls54 wse8">A<span class="_3e blank"> </span>B<span class="_64 blank"> </span>A <span class="ff4 ls1b5">\u2212</span><span class="ls1b6">B<span class="ff1 ls1b7">=</span></span><span class="ws5">z<span class="ff3 fs1 ls1b8 va">1</span><span class="ls1b9">A<span class="ff1 ls1ba">+</span><span class="ls1b6">B<span class="ff1 ls1b7">=</span></span></span>z<span class="ff3 fs1 va">2</span></span></div><div class="t m0 x82 h5 y119 ff2 fs0 fc0 sc0 ls62">A<span class="ff1 ls54 ws0">= (</span><span class="ls54 ws5">z<span class="ff3 fs1 ls45 va">2</span><span class="ff1 ls2e">+</span>z<span class="ff3 fs1 ls2f va">1</span><span class="ff1 ws6">)</span>/<span class="ff1 ls63">2</span><span class="ls1bb">B</span><span class="ff1 ws0">= (</span>z<span class="ff3 fs1 ls45 va">2</span><span class="ff4 lsb">\u2212</span>z<span class="ff3 fs1 ls2f va">1</span><span class="ff1 ws6">)</span>/<span class="ff1">2</span></span></div><div class="t m0 xa8 h2 y11a ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls38 va">1</span></span><span class="ls39">)<span class="ff4 lsb">\u2212</span></span>cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">2</span></span><span class="ws0">) = 2<span class="_4f blank"> </span>sen(<span class="_59 blank"> </span><span class="ff2 ws5 v1">z</span><span class="ff3 fs1 ls45 v1e">2</span><span class="ls2e v1">+</span><span class="ff2 ws5 v1">z</span><span class="ff3 fs1 v1e">1</span></span></div><div class="t m0 xa9 h20 y11b ff1 fs0 fc0 sc0 ls1bc">2<span class="ls54 wse9 v1">)<span class="_4f blank"> </span>sen( </span><span class="ff2 ls54 ws5 v2">z</span><span class="ff3 fs1 ls45 v26">2</span><span class="ff4 lsb v2">\u2212<span class="ff2 ls54 ws5">z<span class="ff3 fs1 va">1</span></span></span></div><div class="t m0 xaa h21 y11b ff1 fs0 fc0 sc0 ls1bd">2<span class="ls54 v1">)</span></div><div class="t m0 xab h3b y11c ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="wsea">) = cos(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">2</span></span><span class="wseb">)<span class="_65 blank"> </span>sen( <span class="ff6 fs1 ls1be v5">z</span><span class="ffa fs2 ls1bf v27">2</span><span class="ff3 fs1 ws3d v5">+<span class="ff6 ls1be">z</span></span><span class="ffa fs2 v27">1</span></span></span></div><div class="t m0 xac h3c y11d ff3 fs1 fc0 sc0 ls1c0">2<span class="ff1 fs0 ls54 wsea v4">) = 0<span class="_3a blank"> </span>sen(<span class="_59 blank"> </span></span><span class="ff6 ls1be v12">z</span><span class="ffa fs2 ls1bf v28">2</span><span class="ff7 ls54 ws13 v12">\u2212<span class="ff6 ls1be">z<span class="ffa fs2 ls54 v29">1</span></span></span></div><div class="t m0 xad h16 y11d ff3 fs1 fc0 sc0 ls1c0">2<span class="ff1 fs0 ls1c1 wsec v4">)=0<span class="_2b blank"></span></span></div><div class="t m0 x62 h2e y11e ff6 fs1 fc0 sc0 ls1be">z<span class="ffa fs2 ls1bf v29">2</span><span class="ff3 ls29">+</span>z<span class="ffa fs2 ls54 v29">1</span></div><div class="t m0 x19 h3d y11f ff3 fs1 fc0 sc0 ls1c2">2<span class="ff1 fs0 ls18 v4">=<span class="ff2 ls54 wsed">k \u03c0<span class="_11 blank"> </span>k<span class="_18 blank"> </span></span></span><span class="ff6 ls1be v12">z</span><span class="ffa fs2 ls1bf v28">2</span><span class="ff7 ls29 v12">\u2212<span class="ff6 ls1be">z<span class="ffa fs2 ls54 v29">1</span></span></span></div><div class="t m0 x44 h14 y11f ff3 fs1 fc0 sc0 ls1c3">2<span class="ff1 fs0 ls18 v4">=<span class="ff2 ls54 wse3">k \u03c0<span class="_11 blank"> </span>k</span></span></div><div class="t m0 x22 h5 y120 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="ws0">) =<span class="_1d blank"> </span>sen(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">2</span></span><span class="ls1ae">)</span><span class="ff2 ws5">z<span class="ff3 fs1 ls1c va">2</span></span><span class="ls18">=</span><span class="ff2 ws5">z<span class="ff3 fs1 ls45 va">1</span><span class="ff4 ls27">±</span></span></span>2<span class="ff2 wsee">n\u03c0 z<span class="ff3 fs1 ls1c va">2</span></span><span class="ls18">=</span><span class="ff4 ws8">\u2212<span class="ff2 ws5">z<span class="ff3 fs1 ls45 va">1</span></span><span class="lsb">±</span></span>(2<span class="ff2 ls4b">n</span><span class="ws1">+ 1)<span class="ff2 wsef">\u03c0<span class="_11 blank"> </span>n </span><span class="ws0">= 0<span class="ff2 ls1f">,</span></span></span>1<span class="ff2 ls1f">,</span>2<span class="ff2 ws11">, . . .</span></div><div class="t m0 x71 h5 y121 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls1c4">A</span><span class="ls1c5">+<span class="ff2 ls1b1">B</span></span><span class="ws66">) =<span class="_66 blank"> </span>sen(<span class="ff2 ls1b4">A</span><span class="ws23">) cos(<span class="ff2 ls5e">B</span><span class="wsf0">) +<span class="_67 blank"> </span>sen(<span class="ff2 ls5e">B</span></span>) cos(<span class="ff2 ws5">A</span><span class="ls1c6">)</span><span class="ff2 wsf1">A B</span></span></span></div><div class="t m0 xa2 h5 y122 ff2 fs0 fc0 sc0 ls5d">A<span class="ff1 ls2e">+</span><span class="ls1bb">B<span class="ff1 ls18">=</span><span class="ls54 ws5">z<span class="ff3 fs1 ls1c7 va">1</span></span></span>A<span class="ff4 ls27">\u2212</span><span class="ls1bb">B<span class="ff1 ls13">=</span><span class="ls54 ws5">z<span class="ff3 fs1 va">2</span></span></span></div><div class="t m0 x5b h5 y123 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">1</span></span><span class="ls39">)<span class="ff4 ls5a">\u2212</span></span>sen(<span class="ff2 ws5">z<span class="ff3 fs1 ls2f va">2</span></span><span class="ws0">) =<span class="_1d blank"> </span>sen(<span class="ff2 ls5d">A</span><span class="ls2e">+<span class="ff2 ls5e">B</span></span><span class="ws1">) +<span class="_3 blank"> </span>sen(<span class="ff2 ls5d">A<span class="ff4 lsb">\u2212</span><span class="ls5e">B</span></span></span>) = 2<span class="_4f blank"> </span>sen(<span class="ff2 ws5">A</span><span class="ws23">) cos(<span class="ff2 ls1b1">B</span>)</span></span></div><div class="t m0 x8c h5 y124 ff1 fs0 fc0 sc0 ls54 ws6">cos(<span class="ff2 ls3">z</span><span class="ws47">) = 2</span></div><div class="t m0 xae h5 y125 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls3">z</span><span class="ws47">) = cosh(4)</span></div><div class="t m0 x22 h5 y126 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls8d">x</span><span class="ws23">) senh(<span class="ff2 ls8e">y</span><span class="wscc">) cos(2<span class="ff2 ls8f">x</span></span>) senh(2<span class="ff2 ls91">y</span>)</span></div><div class="t m0 x3c h5 ye8 ff1 fs0 fc0 sc0 ls54 ws6">sen(<span class="ff2 ls3">z</span><span class="wscc">) cos(<span class="ff2 ls3">z</span>)</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2a y0 w3 h17" alt="" src="https://files.passeidireto.com/d27d4a78-7f55-48cf-b486-127063f90ef1/bga.png"><div class="t m0 x8a h5 y29 ff1 fs0 fc0 sc0 ls54 ws6">senh(<span class="ff2 ls1c8">z</span><span class="ls1c9">+</span><span class="ff2 ws46">\u03c0 \u0131</span><span class="ws67">) = <span class="ff4 ls185">\u2212</span></span>senh(<span class="ff2 ls3">z</span><span class="wsf2">) cosh(<span class="ff2 ls1c8">z</span><span class="ls1c9">+</span><span class="ff2 ws46">\u03c0 \u0131</span><span class="ws67">) = <span class="ff4 ls185">\u2212</span></span></span>cosh(<span class="ff2 ls3">z</span><span class="wsf3">) tgh(<span class="ff2 ls1ca">z</span><span class="ls1cb">+</span><span class="ff2 ws46">\u03c0 \u0131</span><span class="ws0">) =</span></span></div><div class="t m0 x1a h5 y2a ff1 fs0 fc0 sc0 ls54 ws6">tgh(<span class="ff2 ls3">z</span>)</div><div class="t m0 xaf h5 y127 ff1 fs0 fc0 sc0 ls54 ws6">senh(<span class="ff2 ls7">z</span><span class="wsf4">) cosh(<span class="ff2 ls3">z</span>)</span></div><div class="t m0 x31 h2 y128 ff1 fs0 fc0 sc0 ls54 ws6">cosh(<span class="ff2 ls3">z</span><span class="ws0">) =<span class="_3 blank"> </span><span class="v1">1</span></span></div><div class="t m0 x8 h2f y129 ff1 fs0 fc0 sc0 ls1cc">2<span class="ls54 ws6 v1">senh(<span class="ff2 ls7">z</span><span class="ws4e">) = <span class="ff2 ls1cd">\u0131</span></span>cosh(<span class="ff2 ls7">z</span><span class="ws4e">) = <span class="ff4 ls14">\u2212</span>2</span></span></div><div class="t m0 xa5 h10 y12a ff2 fs0 fc0 sc0 ls1ce">w<span class="ff1 ls54 wsf5">= senh(</span><span class="ls7">z<span class="ff3 fs1 ls2f v5">2</span><span class="ff1 ls1cf">)</span><span class="ls54 wsf6">x y</span></span></div><div class="t m0 x9e h5 y12b ff2 fs0 fc0 sc0 ls42">n<span class="ff1 ls54 ws0">= 0</span><span class="ls1f">,<span class="ff1 ls54 ws6">1</span>,<span class="ff1 ls54 ws6">2</span><span class="ls54 ws11">, . . .</span></span></div><div class="t m0 xe h1a y12c ff1 fs0 fc0 sc0 ls54 ws10">log(1)<span class="_4 blank"> </span>=<span class="_4 blank"> </span><span class="ff4 ws8">±</span><span class="ws6">2<span class="ff2 ws46">n\u03c0 \u0131<span class="_7 blank"> </span></span></span>log (<span class="ff4 ws8">\u2212</span><span class="wsf7">1) = <span class="ff4 ls14">±</span><span class="ws6">(2<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ws46">\u03c0 \u0131<span class="_1e blank"> </span></span></span></span></span>log (<span class="ff2 ws5">\u0131</span><span class="ws0">) =<span class="_3 blank"> </span><span class="ff6 fs1 v5">\u03c0</span></span></div><div class="t m0 x5c h3e y12d ff3 fs1 fc0 sc0 ls187">2<span class="ff2 fs0 ls1d0 v4">\u0131<span class="ff4 lsb">±<span class="ff1 ls54 ws6">2<span class="ff2 ws46">n\u03c0 \u0131<span class="_7 blank"> </span></span><span class="ws10">log(<span class="ff2 ws5">\u0131</span></span></span></span></span><span class="ls54 ws3d v13">1<span class="ff6 ws20">/<span class="ff3 ls38">2</span><span class="ff1 fs0 ws0 v20">) =<span class="_3 blank"> </span></span><span class="v0">\u03c0</span></span></span></div><div class="t m0 xb0 h14 y12d ff3 fs1 fc0 sc0 ls187">4<span class="ff2 fs0 ls1d0 v4">\u0131<span class="ff4 lsb">±<span class="ff2 ls54 ws46">n\u03c0 \u0131</span></span></span></div><div class="t m0 x88 h5 y12e ff1 fs0 fc0 sc0 ls54 ws10">log(<span class="ff2 ls3">z</span>)<span class="_68 blank"> </span>log(<span class="ff2 ls7">z</span><span class="wsf8">) = ln<span class="_4f blank"> </span><span class="ff4 ws8">|<span class="ff2 ls7">z</span><span class="ls1d1">|</span></span><span class="ls1d2">+<span class="ff2 ls31">\u0131</span></span></span>arg (<span class="ff2 ls3">z</span><span class="ls1d3">)<span class="ff2 ls1d4">z</span></span><span class="ff4 ws8">6</span><span class="wsf8">= 0<span class="_40 blank"> </span>ln</span></div><div class="t m0 xb1 h3f y12f ff1 fs0 fc0 sc0 ls54 ws6">ln(<span class="ff2 lsf5">r</span><span class="ws4e">) = <span class="ff5 ls1d5 v2">Z</span><span class="ff6 fs1 v3">r</span></span></div><div class="t m0 xa7 h40 y130 ff3 fs1 fc0 sc0 ls54">1</div><div class="t m0 xb2 h5 y131 ff1 fs0 fc0 sc0 ls54">1</div><div class="t m0 xb2 h21 y132 ff2 fs0 fc0 sc0 ls1d6">t<span class="ls54 wsf9 v1">dt<span class="_60 blank"> </span>r<span class="_69 blank"> </span>> <span class="ff1">0</span></span></div><div class="t m0 x27 h1a y133 ff1 fs0 fc0 sc0 ls54 ws10">Log(<span class="ff4 ls185">\u2212</span><span class="ls1d7">e</span><span class="ff2 ws5">\u0131</span><span class="lsc6 ws6e">)=1<span class="_6a blank"></span><span class="ff4 ls153">\u2212<span class="ff6 fs1 ls54 v5">\u03c0</span></span></span></div><div class="t m0 xae h35 y134 ff3 fs1 fc0 sc0 ls187">2<span class="ff2 fs0 ls1d8 v4">\u0131<span class="ff1 ls54 ws10">Log(1<span class="_6 blank"> </span><span class="ff4 lsb">\u2212</span><span class="ff2 ws5">\u0131</span><span class="ws0">) =<span class="_3 blank"> </span></span></span></span><span class="ls54 v12">1</span></div><div class="t m0 xa9 h36 y134 ff3 fs1 fc0 sc0 ls1d9">2<span class="ff1 fs0 ls54 wsfa v4">ln(2) <span class="ff4 ls153">\u2212</span></span><span class="ff6 ls54 v12">\u03c0</span></div><div class="t m0 xb3 h14 y134 ff3 fs1 fc0 sc0 ls187">4<span class="ff2 fs0 ls54 v4">\u0131</span></div><div class="t m0 x12 h5 y135 ff1 fs0 fc0 sc0 ls54 ws10">Log(<span class="ff2 ls7">z</span>)<span class="_6b blank"> </span>Log(<span class="ff2 ls3">z</span><span class="ws0">) =</span></div><div class="t m0 x1a h5 y136 ff1 fs0 fc0 sc0 ls54 ws6">ln(<span class="ff2 lsf5">r</span><span class="ws1">) + <span class="ff2 wse">\u0131\u03b8<span class="_4e blank"> </span>z </span><span class="ls13">=<span class="ff2 lse4">r</span></span><span class="ff4 ws8">{</span></span>cos(<span class="ff2 ls48">\u03b8</span><span class="ws1">) + <span class="ff2 ls31">\u0131</span></span>sen(<span class="ff2 ls48">\u03b8</span>)<span class="ff4 ls1da">}</span><span class="ff2 wsfb">r<span class="_69 blank"> </span>> </span><span class="ls63">0<span class="ff4 ls14">\u2212</span></span><span class="ff2 wsfc">\u03c0<span class="_a blank"> </span>< \u03b8<span class="_69 blank"> </span><span class="ff4 ls43">\u2264</span>\u03c0</span></div><div class="t m0 x8c h41 y137 ff1 fs0 fc0 sc0 ls54 ws10">log(<span class="ff2 ls7">z</span><span class="ws0">) =<span class="_3 blank"> </span><span class="ff6 fs1 v5">\u03c0</span></span></div><div class="t m0 xf h16 y138 ff3 fs1 fc0 sc0 ls187">2<span class="ff2 fs0 ls54 v4">\u0131</span></div><div class="t m0 xae hb y139 ff1 fs0 fc0 sc0 lsf2">e<span class="ff6 fs1 ls1db v5">z</span><span class="ls13">=<span class="ff4 ls14">\u2212</span><span class="ls54">3</span></span></div><div class="t m0 xb4 h10 y13a ff1 fs0 fc0 sc0 ls54 ws6">ln(<span class="ff2 ls8d">x<span class="ff3 fs1 ls1dc v5">2</span></span><span class="ls1dd">+<span class="ff2 ls91">y<span class="ff3 fs1 ls2f v5">2</span></span></span>)</div><div class="t m0 xb5 h10 y13b ff4 fs0 fc0 sc0 ls54 ws8">\u2207<span class="ff3 fs1 ls38 v5">2</span><span class="ff2 ls1de">u</span><span class="ff1 wsfd">= 0</span></div><div class="t m0 xb6 h5 y13c ff2 fs0 fc0 sc0 ls1df">x<span class="ff1 ls1e0">=</span><span class="lse1">r<span class="ff1 ls54 ws6">cos(</span><span class="ls10">\u03b8<span class="ff1 ls54 ws6">)</span><span class="ls54 ws11">, y<span class="_a blank"> </span><span class="ff1 ls1e1">=</span><span class="ls1e2">r</span><span class="ff1 ws6">sen(</span><span class="ls48">\u03b8</span><span class="ff1">)</span></span></span></span></div><div class="t m0 x1a h10 y13d ff2 fs0 fc0 sc0 ls1e3">u<span class="ff1 ls54 ws86">= ln(</span><span class="ls8d">x<span class="ff3 fs1 ls1e4 v5">2</span><span class="ff1 ls1e5">+</span><span class="ls91">y<span class="ff3 fs1 ls2f v5">2</span><span class="ff1 ls54 wsfe">) = ln(</span><span class="lsf5">r<span class="ff3 fs1 ls38 v5">2</span><span class="ff1 ls54 ws23">)<span class="_1d blank"> </span>=<span class="_1d blank"> </span>2 ln(</span>r<span class="ff1 ls1e6">)</span><span class="lsa5">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54 wsfe">) = ln(</span><span class="lse4">r<span class="ff1 ls54 wsff">) + <span class="ff2">\u0131\u03b8</span></span></span></span></span></span></span></span></div><div class="t m0 xb7 h5 y13e ff2 fs0 fc0 sc0 ls23">z<span class="ff1 ls54 ws0">= 0<span class="_6c blank"> </span><span class="ff2">f</span></span></div><div class="t m0 x40 h5 y13f ff2 fs0 fc0 sc0 ls1e7">u<span class="ff1 ls54 ws6">2</span><span class="lsa7">f<span class="ff1 ls54 ws6">(</span><span class="ls3">z<span class="ff1 ls54">)</span></span></span></div><div class="t m0 x1a h5 y140 ff2 fs0 fc0 sc0 ls1e8">u<span class="ff1 ls54 ws6">(</span><span class="ls8f">x<span class="ff6 fs1 lsa8 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 lsa8 va">o</span><span class="ff1">)</span></span></span></div><div class="t m0 xb8 h5 y141 ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 ls8d">x<span class="ff6 fs1 ls102 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 lsa8 va">o</span></span></span>)</div><div class="t m0 x1a h5 y142 ff1 fs0 fc0 sc0 ls2a">(<span class="ff2 ls8d">x<span class="ff6 fs1 lsa8 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 lsa8 va">o</span></span></span><span class="ls54 ws100">) 2<span class="ff2 lsa7">f</span></span>(<span class="ff2 ls7">z</span><span class="ls1e9">)<span class="ff2 ls1ea">u</span><span class="ls54 ws6">2<span class="ff2 lsa7">f</span>(<span class="ff2 ls3">z</span><span class="ls1eb">)</span><span class="ff2">u</span></span></span></div><div class="t m0 xb9 h5 y143 ff1 fs0 fc0 sc0 ls54 ws6">(<span class="ff2 ls8d">x<span class="ff6 fs1 ls102 va">o</span><span class="ls54 ws11">, y<span class="ff6 fs1 ls102 va">o</span></span></span>)</div><div class="t m0 x9e h5 y144 ff2 fs0 fc0 sc0 ls42">n<span class="ff1 ls54 ws0">= 0</span><span class="ls1f">,<span class="ff1 ls54 ws6">1</span>,<span class="ff1 ls54 ws6">2</span><span class="ls54 ws11">, . . .</span></span></div><div class="t m0 xba hb y145 ff1 fs0 fc0 sc0 ls54 ws1">a)<span class="_4 blank"> </span>(1 + <span class="ff2 ws5">\u0131</span><span class="ls2a">)<span class="ff6 fs1 ls1ec v5">\u0131</span></span><span class="ws0">= exp(<span class="ff4 lsf8">\u2212</span><span class="ff6 fs1 v5">\u03c0</span></span></div><div class="t m0 xaf h35 y146 ff3 fs1 fc0 sc0 ls1ed">4<span class="ff4 fs0 lsb v4">±<span class="ff1 ls54 ws6">2<span class="ff2 ws101">n\u03c0 </span><span class="ws102">)<span class="_4f blank"> </span>exp( </span></span></span><span class="ls54 v12">1</span></div><div class="t m0 xbb h3e y146 ff3 fs1 fc0 sc0 ls1ee">2<span class="ff1 fs0 ls54 ws6 v4">ln(2)<span class="ff2 ws5">\u0131<span class="ff1 ws0">)<span class="_6d blank"> </span>b) (<span class="ff4 ws8">\u2212</span></span></span>1)</span><span class="ls54 ws3d v13">1<span class="ff6 ws103">/\u03c0 <span class="ff1 fs0 ws0 v20">= exp(<span class="ff4 ws8">±<span class="ff1 ws6">(2<span class="ff2 ls53">n</span><span class="ws1">+ 1)<span class="ff2 ws5">\u0131</span>)</span></span></span></span></span></span></div><div class="t m0 x2b hb y147 ff1 fs0 fc0 sc0 ls54 ws104">a) <span class="ff2 ws5">\u0131<span class="ff6 fs1 ls1ef v5">\u0131</span></span><span class="ws105">b)<span class="_4 blank"> </span>( <span class="ff3 fs1 v5">e</span></span></div><div class="t m0 xf h42 y148 ff3 fs1 fc0 sc0 ls18b">2<span class="ff1 fs0 ls54 ws6 v4">(<span class="ff4 ls14">\u2212<span class="ff1 ls25">1</span><span class="lsb">\u2212<span class="ff2 ls54 ws5">\u0131</span><span class="ls21 v9">\u221a</span></span></span>3))</span><span class="ls54 ws3d v13">3<span class="ff6 wsca">\u03c0 \u0131<span class="_24 blank"> </span><span class="ff1 fs0 ws106 v20">c)<span class="_4 blank"> </span>(1 <span class="ff4 lsb">\u2212<span class="ff2 ls54 ws5">\u0131</span></span><span class="ws6">)</span></span><span class="ff3 ls68">4</span>\u0131</span></span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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