If ω,ω2,ω3,........ωn−1 are nth roots of unity then (1−ω)(1−ω2).......(1−ωn−1) 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 Cn Since 1,ω,ω2,ω3,.........ωn−1 are nth roots of unity, therefore, we have the identity (x−1)(x−ω)(x−ω2)......(x−ωn−1) =xn−1 or (x−ω)(x−ω2)......(x−ωn−1)=xn−1x−1 =xn−1+xn−2+......+x+1 Putting x = 1 on both sides, we get (1−ω)(1−ω2)(1−ωn−1)=n