## Polar form.

Let , where and .

The precise meaning of the last equation, namely of

is that there exist exactly distinct roots for any non zero complex number . You can check this by the following way: let increase from 0 to , you have distinct numbers. From and further on, you get the same complex numbers again (you only added a multiple of to the argument...).

Example 1.5.2   Find the cubic roots of .

. Thus:

The cubic roots of are:

Example 1.5.3   Find the cubic roots of .

. Thus:

The cubic roots of are:

 and

Noah Dana-Picard 2007-12-24