Definition:Complex Number/Polar Form/Exponential Form

Definition

Let $z := \polar {r, \theta}$ 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.

Also known as

Some sources refer to the form $z = r e^{i \theta}$ as polar form, and do not feel the need to treat it as a different representation from the $z = r \paren {\cos \theta + i \sin \theta}$ form.