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Math Help - Complex integral.

  1. #1
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    Complex integral.

    Evaluate the complex integral:
    \oint _c\frac{e^{3z}}{z - \pi i}dz

    If C is the ellipse |z-2| + |z+2| = 6

    The integral is zero by Cauchy's Theorem as the point \pi i is outside of the ellipse according to the answer at the back of the book, I just wanted to convince myself how that is the case. Thanks in advance.
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  2. #2
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    Re: Complex integral.

    Sorry what are you trying to convince yourself of? That the point \displaystyle \begin{align*} (0, \pi) \end{align*} doesn't lie inside the ellipse? Can you get the Cartesian equation for the ellipse?
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