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Complex Integrals - Poles of Integration Outside the Curve

  1. Mar 16, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\int_{|z-2i|=2}[/itex] = [itex]\frac{dz}{z^2-9}[/itex]

    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. jcsd
  3. Mar 16, 2012 #2
    Your integrand is analytic in a region that contains your contour, what do you know about a closed contour integral of an analytic function?
  4. Mar 16, 2012 #3
    The integral is 0. Makes sense. Thanks.
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