alleryFor roots of unity ω^n = 1: which is the SMALLEST n such that 1 + ω + ω² + ... + ω^(n-1) = 0?
A2
BOnly n = 3
C1
DAny n > 1
Answer & Solution
Correct answer: D. Any n > 1
Sum 1 + ω + ω² + ...
+ ω^(n-1) = (ω^n - 1)/(ω - 1) = 0 when ω is a primitive n-th root (ω ≠ 1).
**So for any n ≥ 2 (with non-trivial primitive root), sum is 0.**
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