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) $

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]])

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