Question

The product of complex roots of unity is
A. 1+w+w²
B. 1
C.w
D.w²​

Answer 1

Answer:

Roots of unity :-

The sum of all n th n^\text{th} nth roots of unity is always zero for n ≠ 1 n\ne 1 n=1. The product of all n th n^\text{th} nth roots of unity is always ( − 1 ) n + 1 (-1)^{n+1} (−1)n+1. 1 1 1 and − 1 -1 −1 are the only real roots of unity. If a number is a root of unity, then so is its complex conjugate.

Answer 2

We know 1+w+w2=01+w+w2=0

—》(1+w2−w)=−2w—》(1+w2−w)=−2w

—》(1−w2+w)=−2w2—》(1−w2+w)=−2w2

—》(1+w2−w)(1−w2+w)—》(1+w2−w)(1−w2+w) =4w3=4×1=4=4w3=4×1=4

(Since w3=1w3=1)

hope this helps you

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