# Homework Help: Residue of cos(z)/z

1. Oct 19, 2009

### HappyEuler2

1. The problem statement, all variables and given/known data
So the problem at hand is to calculate the contour integral $$\oint$$ 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?

2. Oct 19, 2009

### Dick

If f(z) has a simple pole at z=c then the residue is lim z->c of (z-c)*f(z), isn't it? What does that give you?

3. Oct 19, 2009

### HappyEuler2

Ah, thank you. I just needed someone to write it out clearly for me.

So the formal answer =2*Pi*i

Last edited: Oct 19, 2009
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