# Definition:Complex Number/Polar Form/Exponential Form

## Definition

Let $z := \left \langle {r, \theta} \right \rangle$ be a complex number in polar form.

From Euler's Formula:

$e^{i \theta} = \cos \theta + i \sin \theta$

so $z$ can also be written in the form:

$z = r e^{i \theta}$

This form of presentation of a complex number is known as exponential form.