If α1, α2, ....αn−1 are the nth roots of unity then (1−α1)(1−α2)...(1−αn−1)=
A
-1
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B
n
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C
1
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D
none of these
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Solution
The correct option is B n xn−1=(x−1)(x−α1)(x−α2)...(x−αn−1) xn−1x−1=(x−α1)(x−α2)...(x−αn−1) 1+x+x2+...xn−1=(x−α1)(x−α2)...(x−αn−1) Substituting, x=1 we get (1−α1)(1−α2)...(1−αn−1)=n