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


Anth roots of unity are evenly spaced on the unit circle.
B1 is always the nth root of unity.
CThe number of nth roots of unity is n.
D-1 is always the nth root of unity.

Verified Answer :

Answer:

C, B, and A

-Apex

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:

\(\dfrac{360\degree}{n}\)

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