# MandysNotes

## The Exponential of a Purely Imaginary Number

13 May 2011

Consider the exponential of a purely imaginary number:

$z = i\alpha$

with $\alpha \in \mathbb{R}\ .$

$e^{i\alpha} = \lim_{n \to \infty } (1 + \frac{i\alpha}{n})^{n}$

$= \sum_{k=0}^{\infty }\frac{i\alpha^{k}}{k!} .$