Evaluate the complex integral:

$\displaystyle \oint _c\frac{e^{3z}}{z - \pi i}dz$

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

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.