Complex Analysis (Practice Exam)

[PieceOfPi]

Homework Statement

This question is in my exam review problem from my complex analysis class.
Compute f⁽¹⁰⁰⁾(0)/100!, where f(z) = 1/(1+i-sqrt(2)z).

(f⁽¹⁰⁰⁾(0) means the 100th derivative of f evaluated at 0.)

Homework Equations

Cauchy's integral formula might be helpful.

The answer to this question is -1/(1+i).

The Attempt at a Solution

I thought about using Cauchy's integral formula, but it seems like I need to rewrite f(z) so that I have singularity at 0... or maybe I'm completely missing out.

Thanks!

 

[rakalakalili]

Have you tried writing the function as it's series representation about 0? Then the calculation you are looking for would be the coefficient in front of the z^100 term.