# Complex Integrals - Poles of Integration Outside the Curve

1. Mar 16, 2012

### SirFibonacci

1. The problem statement, all variables and given/known data

$\int_{|z-2i|=2}$ = $\frac{dz}{z^2-9}$

2. The attempt at a solution

I know that the contour described by |z-2i|=2 is a circle with a center of (0,2) (on the complex plane) with a radius of 2. The singularities of the integral fall outside of the contour (z+3 and z-3). In this case, is the solution just going to be zero or undefined?

2. Mar 16, 2012

### sunjin09

Your integrand is analytic in a region that contains your contour, what do you know about a closed contour integral of an analytic function?

3. Mar 16, 2012

### SirFibonacci

The integral is 0. Makes sense. Thanks.