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

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7 years ago

Navjyot Kalra
654 Points
```										Dear Mahima,

Since,1,w,w2,….,wn-1 are the nth roots of unity, therefore
xn-1=(x-1)(x-w)(x-w2)…(x-wn-1)
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 ".
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7 years ago
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