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Question

If α0,α1,α2,,αn1 are nth roots of unity, then

αk=cos(2kπn)+i sin(2kπn); where

0kn1, Also

(xn1)=(xα0)(xα1)(xαn1)

Value of (1+α0)(1+α1)(1+αn1) is

A
3
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B
(1)n
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C
0.0
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D
1+(1)n+1
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Solution

The correct option is D 1+(1)n+1
Put x = -1, so that

(1)n1=(1α0)(1α1)(1αn1)

(1)n[1+(1)n+1)=(1)n(1+α0)(1+α1)(1+αn1)

(1+α0)(1+α1)(1+αn1)=1+(1)n1

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