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Question

If α1, α2, ....αn1 are the nth roots of unity then (1α1)(1α2)...(1αn1)=

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
xn1=(x1)(xα1)(xα2)...(xαn1)
xn1x1=(xα1)(xα2)...(xαn1)
1+x+x2+...xn1=(xα1)(xα2)...(xαn1)
Substituting, x=1 we get
(1α1)(1α2)...(1αn1)=n

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