1. The problem statement, all variables and given/known data So the problem at hand is to calculate the contour integral [tex]\oint[/tex] cos(z)/z around the circle abs(z)=1.5 . 2. Relevant equations The integral is going to follow from the Cauchy-Integral Formula and the Residue theorem. The problem I am having is figuring out what the residue is going to be. 3. The attempt at a solution So I know the pole is at z = 0, which lies inside of the contour. So the integral reduces to I=2*pi*i*residue @ 0. What I can't figure out is how to determine the residue. If I use maple, I know that the residue is 1, but I want to figure out where it comes from it. Any help?