
Complex integral.
Evaluate the complex integral:
$\displaystyle \oint _c\frac{e^{3z}}{z  \pi i}dz$
If C is the ellipse $\displaystyle z2 + z+2 = 6$
The integral is zero by Cauchy's Theorem as the point $\displaystyle \pi i$ 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.

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