$\"\"$

\

The complex number is $\"\"$ .

\

Convert the complex number into polar form.

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The polar form of $\"\"$ is $\"\"$ .

\

$\"\"$

\

Find the fifth roots of $\"\"$ .

\

\

Theorem :

\

If $\"\"$ is a positive integer, the complex number $\"\"$ has exactly $\"\"$ distinct complex $\"\"$ roots.

\

The complex roots are $\"\"$ , where $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The complex fifth roots of $\"\"$ are

\

$\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .