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Question

If a1,a2,....,an1 are the nth roots of unity then the value of (1a1)(1a2)...(1an1) is equal to

A
3
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B
12
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C
n
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D
0
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Solution

The correct option is C n
Since, 1,a1,a2,....,an1 are the nth root of unity.
xn1=(x1)(xa1)...(xan1)
xn1x1=(xa1)(xa2)....(xan1)
xn1+xn2+...+x2+x+1
=(xa1)(xa2)....(xan1)
Put x=1, we get
(1a1)(1a2)...(1ant)=1+1+...+n times
=n.

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