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

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