# How do you convert complex numbers from standard form to polar form and vice versa?

Jul 13, 2018

#### Explanation:

To convert a complex number

$z = x + i y$

to the polar form

$z = r \left(\cos \theta + i \sin \theta\right)$

Apply the following :

$\left\{\begin{matrix}r = | z | = \sqrt{{x}^{2} + {y}^{2}} \\ \cos \theta = \frac{x}{| z |} \\ \sin \theta = \frac{y}{| z |}\end{matrix}\right.$

And to convert

The polar form

$z = r \left(\cos \theta + i \sin \theta\right)$

to the standard form

$z = x + i y$

Apply the folowing

$\left\{\begin{matrix}x = r \cos \theta \\ y = r \sin \theta\end{matrix}\right.$