Describe the behavior of $\displaystyle e^{x + iy}$ as $\displaystyle x \to \pm \infty$ and of $\displaystyle e^{x+iy}$ as $\displaystyle y \to \pm \infty$

This is my answer:

We have $\displaystyle e^{x}(\cos{y} + i\sin{y})$. This implies that if x -> infinity, the function will go to infinity. And, if x -> neg. infty, the function will go to 0. If y goes to pos/neg infty, the function will oscillate.

Thoughts?