Question

Which of the following are correct statements concerning the roots of unity? Check all that apply.


A. nth roots of unity are evenly spaced on the unit circle.
B. 1 is always the nth root of unity.
C. The number of nth roots of unity is n.
D. -1 is always the nth root of unity.

Answer 1

Answer:

C, B, and A

-Apex

Answer 2

Answer:

The correct options are:

A. nth roots of unity are evenly spaced on the unit circle.

B. 1 is always the nth root of unity.

C. The number of nth roots of unity is n.

Step-by-step explanation:

We know that form any complex number 'z' the nth root of unity satisfies the equation:

                        $z^n=1$

• Also, the number of nt roots of unity are n.

• Also, 1 is always a root of the equation.

• and -1 is always a root when n is even.

( Since, if we consider,

$z^3=1$

The roots are:

1,ω,ω² )

• Also, the roots are at a fixed distance or are evenly spaced on a unit circle.

Since they are separated by an angle of:

$\dfrac{360\degree}{n}$