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Question

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

A
0
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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 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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