If 1,ω,ω 2 ,…….ω n-1- are nth roots of unity, then (1-ω)(1-ω 2 )…(1-ω n-1 ) is equal to

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


1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
12 years ago

Dear Mahima,


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


        Þ (x-w)( x-w2)..( x-wn-1)=

Þ (x-w)( x-w2)..( x-wn-1)=1+x+x2+…+xn-1

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

 So the value is equal to " n ". provides online iit jee courses and IIT JEE Test Series with IITians. Click here to get free online test series and check your status timely or you can join us as our registered user for getting best iit jee study material or iit jee test series.

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