Math Help - [SOLVED] Complex Analysis: integrals &amp; residue thereom

1. [SOLVED] Complex Analysis: integrals &amp; residue thereom

Hi there, I'm asked to evaluate the following integral counterclockwise

$\int\limits_{|z| = 2}^{ }({1 - cosz})/({z^2 - z}) dz$

The residue theorem doesn't work, as taking singularities at z = 0 and z = 1, I get 0 as the result for the residue when z = 0. I don't know what else to do, any advice would be appreciated.

2. Originally Posted by pineapple89
Hi there, I'm asked to evaluate the following integral counterclockwise

$\int\limits_{|z| = 2}^{ }({1 - cosz})/({z^2 - z}) dz$

The residue theorem doesn't work, as taking singularities at z = 0 and z = 1, I get 0 as the result for the residue when z = 0. I don't know what else to do, any advice would be appreciated.
try letting $cosz = \frac{1}{2}(z+\frac{1}{z})$ and then tidy up $f(z)$