If
are
nth roots of unity, then for
Text Solution
Verified by ExpertsD
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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