Home Maths Complex Number Skill Builder If are nth roots of unity, then for
Maths Complex Number Skill Builder Single Correct MCQ
Published on: August 13, 2026

If are nth roots of unity, then for

A
B

C
D

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The correct answer is:
D

Let's carefully analyze this.
The th roots of unity are complex numbers satisfying:

These can be written as:

Now, the modulus of any complex number in this form is:

This is true for all , because all nth roots of unity lie on the unit circle in the complex plane.
So for the options:

doesn't make sense because all moduli are 1, and is actually (cyclic), so this is false.

again false because all moduli are 1.

would imply , false.

yes, true, because all have modulus 1.

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