# Complex integral.

• Nov 13th 2013, 09:36 PM
Pupil
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.
• Nov 14th 2013, 01:19 AM
Prove It
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?