If 1,ω,ω2,…,ωn−1 are n, nth roots of unity, the value of (9−ω)9−ω2…9−ωn−1 will be

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9n−18

9n+18

answer is C.

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Detailed Solution

let x=(1)1/nxn−1=0or xn−1=(x−1)(x−ω)x−ω2…x−ωn−1⇒xn−1x−1=(x−ω)x−ω2…x−ωn−1Putting x = 9 in both sides, we have(9−ω)9−ω29−ω3…9−ωn−1=9n−18

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