Consider the following complex analysis definitions and theorems: Definição 11.17 Definição 11.18 Teorema 11.11 Teorema 11.12 Exemplo 11.13 Exe...

Consider the following complex analysis definitions and theorems:
Definição 11.17
Definição 11.18
Teorema 11.11
Teorema 11.12
Exemplo 11.13
Exemplo 11.14
Exemplo 11.15
a) The function f(z) = z/z is not holomorphic at any point in C.
b) The n-th derivative of f(z) = z^n is f(n)(z) = n! for n <= 1 and f(k)(z) = 0 for k >= n+1.
c) The function h1(z) = f(z) + wg(z) is holomorphic at z0 and h1'(z0) = f'(z0) + wg'(z0), where w is a complex number and f and g are holomorphic at z0.
d) The function h3(z) = f(z)/g(z) is differentiable at z0 and h3'(z) = (f'(z0)g(z0) - f(z0)g'(z0))/g(z0)^2, where g(z0) is not equal to 0 and f and g are holomorphic at z0.
e) The limit lim(z->z0) (z-z0)/(z-z0) does not exist for any z0 in C.
f) The function f(z) = z is not continuous at z=0.
g) The function f(z)g(z) is holomorphic at z0 and (f*g)'(z0) = f'(z0)g(z0) + f(z0)g'(z0), where f and g are holomorphic at z0.
a) a, b, c, and d are correct.
b) b, c, d, and g are correct.
c) a, b, e, and f are correct.
d) c, d, e, and g are correct.