Complex numbers are defined as an extension of real numbers by adding an imaginary part i, where $ i=\sqrt{-1} $. This page is meant to help explain how to convert complex numbers between the polar and Cartesian forms, which is very useful in electrical engineering.
Introduction
A complex number in Cartesian form is generally written in the form
$ a+b*i $
In the polar form, a complex number is represented by its absolute value and its angle. If z is a complex number, then the absolute value is defined as
$ r =|z| $
and its angle is defined as
φ=$ \operatorname{atan}(z) $
Conversion
Converting from one system to another is a fairly straightforward process. Converting
$ a+b*i $
to polar is as simple as
$ r=\sqrt{a^2+b^2} $ <--absolute value
φ=$ \operatorname{atan}(a/b) $ <---angle
Here is a numerical example of this process:
Ex:1+i
r=$ \sqrt{1^2+1^2}=\sqrt{2} $ φ=$ \operatorname{atan}(1/1)=\pi/2 $
(Source: Wikipedia - [[1]])
