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.

 Compare the complex number with a + ib.

.

  so, the angle is :

The trigonometric form of is .

Cube roots of  are :

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

The three roots are :

 for k = 0,

for k = 1,

, and

for k = 2,

(b)

The complex roots are plotted as an absolute value of 2 :

(c)

The standard form of the roots:

(a) The three roots are  :

(b) The graph is :

(c) The standard form of the roots: