If n is a positive integer, the complex number has exactly n distinct n th roots.

The roots are , where

(a)

The complex number is .

First convert the complex number into trigonometric form.

The complex number is .

 Compare the complex number with a + ib.

a = 4 and b = .

a = 4  so, the angle is :

The trigonometric form of is .

Fifth roots of are :

, here n = 5 and k = 0, 1, 2, 3 and 4.

The five roots are :

 for k = 0,

for k = 1,

for k = 2,

for k = 3,

and

for k = 4,

(b)

The complex roots are plotted as an absolute value of :

(c)

The standard form of the roots:

(a) The five roots are  :

(b) The graph is :

(c) The standard form of the roots: