# How do I find the #n#th power of a complex number?

##### 1 Answer

You could use the complex number in rectangular form (

What you can do, instead, is to convert your complex number in POLAR form:

Graphically:

so that now the

Let's look at an example:

Suppose you want to evaluate

Using this notation you should evaluate:

But if you change it in polar form you get:

Your number in polar form becomes:

You can now wonder what is the rectangular form of your result.

We get there using the trigonometric form and do some math.

Looking at your

your complex number becomes now:

That gives you:

(I rounded a little bit to make it clearer)