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Question

If 1,ω,ω2,ω3.....,ωn1 are the n,nth roots of unity, then (1ω)(1ω2).....(1ωn1) equals

A
\N
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B
1
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C
n
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D
n2
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Solution

The correct option is C n
Since 1,ω,ω2,ω3,.....ωn1 are the n, nth roots of unity, therefore, we have the identity
=(x1)(xω)(xω2).....(xωn1)=xn1

or (xω)(xω2)....(xωn1)=xn1x1
=xn1+xn2+.....+x+1
Putting x = 1 on both sides, we get
(1ω)(1ω2)....(1ωn1)=n

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