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 DanaPicard
20071224