Chapter 9.3, Problem 62AYU

To determine

To find the six complex sixth roots of unity and plot them.

Answer to Problem 62AYU

The six complex roots of unity are

Explanation of Solution

1 can be written as the complex number

Rewrite 1 in the form

The magnitude of 1,

  

The distinct complex roots of are, where is a complex number, and

The complex roots of are

  

Where

Substitute 0 for in to get the first complex root of 1.

  

Substitute 1 for k in to get the second complex root of 1.

  

Substitute 2 for k in to get the third complex root of 1.

  

Substitute 3 for k in to get the fourth complex root of 1.

  

  and

  

Therefore, the six complex roots of unity are

Plotting the six roots as follows-