Let f(z)=z^3-i and g(z)=(z+i)^2+1 . Which of the following expressions is/are true?

Question

Let   f(z)=z^3-i  and   g(z)=(z+i)^2+1 . Which of the following expressions is/are true?

Accepted Answer

None of the other responses.

Answer

\dfrac{d}{dz}\left(g\left(f(z)\right)\right)=6z^6

Answer

For each   z\in \mathbb{C} ,   f'(z)
e g'(z) .

Answer

g\left(f(2i) \right)=63

Answer

\dfrac{d}{dz}\left(f(z)g(z)\right)=3z^2\left((z-i)^2 + 1\right) - 2(z^3 - i)(z + i)

Answer

f'(2i)+g'(3)=-6+4i

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