Chapter 6.5, Problem 102E

To determine

To find all solutions of the equation and represent the solutions graphically.

Explanation of Solution

The given expression is

  

This can be written as

  

It means to find sixth roots of the complex number

Writing in standard trigonometric form as follows-

  

Using the formula for nth roots of a complex number which states that,

For a positive integer the complex number has exactly distinct roots given by,

  

Where.

  

Using the above formula,

  

So, for roots are as follows

For 0,

  

For 1,

  

For 2,

  

For 3,

  

Representing the solutions graphically.