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

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

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Grade:11

2 Answers

Arun
25750 Points
6 years ago
Dear Sunny
 
Put x=1 on both the sides nowAns =3x^2 + x +1= (x-a_1)(x-a_2).....(x-a_{n-1})\frac{x^3 -1}{(x-1)}= (x-a_1)(x-a_2).....(x-a_{n-1})x^3 -1= (x-1)(x-a_1)(x-a_2).....(x-a_{n-1}) – 1 =0So I can write3Basically 1,a1,a2......an-1 all these are the roots of this equation x
 
regards
Arun(askIITians forum expert)
Aaditya khosya
13 Points
5 years ago
Let n=4 , then
1,w,w² are the complex root of unity 
So (1-w)(1-w²)= 1-w-w²-w³
Now as we know that w³= 1
 So in equation 1-w-w²-1= -w²-w = 1

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