Answer to Question #201210 in Complex Analysis for anuj

Question

Evaluate integral of (z-3)^4 where c is the circle |z-3|=4

Answer 1

By Cauchy's integral theorem:

$\oint_Lf(z)dz=0$

So:

$\oint_{|x-3|=4}(z-3)^4dz=0$