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, which is sometimes considered one of most beautiful equations in mathematics:

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