If 1,ω,ω2,…….ωn-1- are nth roots of unity, then (1-ω)(1-ω2)…(1-ωn-1) is equal to

Dear Mahima,

Since,1,w,w²,….,w^n-1 are the nth roots of unity, therefore

        xⁿ-1=(x-1)(x-w)(x-w²)…(x-w^n-1)

        Þ (x-w)( x-w²)..( x-w^n-1)=

Þ (x-w)( x-w²)..( x-w^n-1)=1+x+x²+…+x^n-1

        Putting x=1 in above equation, we have (1-w)(1-w²)….(1-w^n-1)=n

 So the value is equal to " n ".

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