EXA1-ALINEAL-GF-RAÚL ANDRÉS GUILLÉN RANGEL-IMKT-MARZO-JULIO 2021

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Raúl Andrés Guillén Rangel 20030941 
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INSTITUTO TECNOLÓGICO DE CELAYA 
INGENIERÍA MECATRÓNICA 
GRUPO A 
ÁLGEBRA LINEAL 
SARA MARCELA ARELLANO DÍAZ 
RAÚL ANDRÉS GUILLÉN RANGEL 
No. De Control 20030941 
EVIDENCIA EXAMEN 
 
Raúl Andrés Guillén Rangel 20030941 
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1. (3 + 5𝑖) + (2 − 3𝑖) 2, 7, 10,16, 24, 25, 26 
5 + 2𝑖 
 
2. 𝑥2 − 2𝑥 + 2 = 0 
𝑥 =
2 ± √(−2)2 − 4(1)(2)
2(1)
 
𝑥 =
2 ± √4 − 8
2
 
𝑥 =
2 ± √−4
2
 
𝑥 =
2 ± 2i
2
 
𝑥 = 1 ± 𝑖 
 
3. 𝑥2 + 𝑥 + 1 
 
4. (3 + 5𝑖) + (2 − 3𝑖) 
 
5 + 2𝑖 
 
 
5. 7𝑖 − (4 + 5𝑖) 
−4+ 2𝑖 
 
6. 3(2 + 4𝑖) 
6 + 12𝑖 
 
7. 
3
1+𝑖
 
(
3
1 + 𝑖
) (
1 − 𝑖
1 − 𝑖
) 
3 − 3𝑖
1 + 1
 
Raúl Andrés Guillén Rangel 20030941 
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3 + 3𝑖
2
 
 
8. 
1
𝑖
 
(
1
𝑖
) (
−𝑖
−𝑖
) 
−𝑖
1
 
−𝑖 
 
9. 
(4+7𝑖)
(2+5𝑖)
 
(
4 + 7𝑖
2 + 5𝑖
) (
2 − 5𝑖
2 − 5𝑖
) 
8 − 20𝑖 + 14𝑖 + 35
4 + 25
 
43 − 6𝑖
29
 
 
10. 
4
(1+2𝑖)2
 
4
−3 + 4𝑖
 
(
4
−3 + 4𝑖
) (
−3 − 4𝑖
−3 − 4𝑖
) 
−12 − 16𝑖
9 + 16
 
−12 − 16𝑖
25
 
 
11. 4 + 5𝑖 = 𝑧 − (1 − 𝑖) 
𝑧 = 5 + 4𝑖 
 
 
 
Raúl Andrés Guillén Rangel 20030941 
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12. (1 + 2𝑖)𝑧 = 2 + 5𝑖 
𝑧 =
2 + 5𝑖
1 + 2𝑖
 
𝑧 = (
2 + 5𝑖
1 + 2𝑖
) (
1 − 2𝑖
1 − 2𝑖
) 
𝑧 =
2 − 4𝑖 + 5𝑖 + 10
1 + 4
 
𝑧 =
12 + 𝑖
5
 
 
13. 3 + 4𝑖 
 
14. 𝐶𝑖𝑠𝛼 = 𝐶𝑜𝑠𝛼 + 𝑖𝑆𝑖𝑛𝛼 
 
15. Verdadero 
 
16. 2√3 + 2𝑖 
𝑟 = √22 + 2√3
2
 
𝑟 = 4 
𝜃 = 𝑡𝑎𝑛−1
2
2√3
 
𝜃 =
𝜋
6
 
4𝐶𝑜𝑠
𝜋
6
+ 4𝑖𝑆𝑖𝑛
𝜋
6
 
 
17. 
 
18. Verdadero 
 
19. Falso 
 
Raúl Andrés Guillén Rangel 20030941 
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20. Verdadero 
 
21. 𝑧 = 3 + 2𝑖 
𝑧𝑜𝑝𝑢𝑒𝑠𝑡𝑜 = −3 − 2𝑖 
 
22. 𝑧 = −3 + 5𝑖 
𝑧𝑜𝑝𝑢𝑒𝑠𝑡𝑜 = 3 − 5𝑖 
23. Falso 
 
24. 230°
3 
(23)3∗30° 
890° 
 
25. 𝑡 = 4𝑖 
𝑟 = √02 + 42 
𝑟 = 4 
𝜃 = 𝑡𝑎𝑛−1
4
0
 
𝜃 = 270° 
4270° 
 
26. √1
6
 
𝑟 = √12 + 02 
𝑟 = 1 
𝑟′ = √1
6
 
𝜃 = 𝑡𝑎𝑛−1
0
1
 
𝜃 = 0° 
𝑟′𝜃2 = √1
6
0°+360°𝑘
6
 
Raúl Andrés Guillén Rangel 20030941 
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𝑧1
′ = √1
6
0° 
𝑧2
′ = √1
6
0° 
𝑧3
′ = √1
6
360°
6
 
𝑧4
′ = √1
6
360°
6
 
𝑧5
′ = √1
6
360°
6
 
𝑧6
′ = √1
6
360°
6