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Question

If α is a non real root of z=(1)1/5, then the value of (1+α+α2+α2α1) is

A
2
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B
2α
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C
2α4
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D
α4
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Solution

The correct option is C 2α4
Let, 1,α,α2,α3,α4 be the roots of z5=1 and,
E=1+α+α2+1α21α
E=α2+α3+α4+1αα2
E=(1+α+α2+α3+α4)2αα2
We know that, sum of n roots of unity is zero, so
E=02αα2=2α
E=2α4

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