# Euler's Formula

Euler's formula is the following identity in complex analysis making use of the imaginary number i:

$e^{i\phi} = \cos \phi + i\sin \phi \!$

## Euler's Identity

The formula can be used to derive an equation known as Euler's identity:

$e^{i\pi} + 1 = 0 \!$

This is called the most beautiful equation in mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner.