Limit at Infinity of Polynomial over Complex Exponential

Theorem
Let $P_n$ be a real polynomial, of degree $n$.

Let $e^z$ be the complex exponential, where $z = x + iy$.

Then for every $n \in \N_{\ge 0}$:


 * $\displaystyle \lim_{x \mathop \to +\infty} \frac {P_n}{e^z} = 0$

Proof
The result then follows from Exponential Dominates Polynomial.