First slide
De-moivre's theorem
Question

If 1,ω,ω2,,ωn1 are n, nth roots of unity, the value of (9ω)9ω29ωn1 will be

Moderate
Solution

let  x=(1)1/nxn1=0or  xn1=(x1)(xω)xω2xωn1xn1x1=(xω)xω2xωn1

Putting x = 9 in both sides, we have

(9ω)9ω29ω39ωn1=9n18

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