# Convert complex number from one representation form to another online with step by step solution

This calculator allows one to convert complex number from one representation form to another with step by step solution. For example, you can convert complex number from algebraic to trigonometric representation form or from exponential back to algebraic, ect. First of all one need to choose representation form of complex number and input data to the calculator. Not only numbers and fractions are allowed as inputs, but also the symbols (parameters) are accepted. Below, represented some theoretical background of the different representation forms of complex numbers.

Expression

z=x+i∙y,

where x, y - arbitrary real numbers is called *algebraic form of complex number*.

Expression

z=r(cosφ + i∙sinφ) (r≥0),

where

is called *trigonometric form of complex number*.

Finally, using Euler formula:

e^{i
φ} =
cosφ
+ i∙sinφ ,

one can get *exponential representation of complex number*:

z=r
e^{i∙
φ}