Complex Exponential Tends to Zero

Theorem
Let $\exp z$ be the complex exponential.

Then:


 * $\displaystyle \lim_{\operatorname{Re} \left({z}\right) \mathop \to +\infty} \exp \left({-z}\right) = 0$

where $\operatorname{Re} \left({z}\right)$ denotes the real part of $z$.

Proof
Let $z = x + iy$.