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Question

If α is a non-real root of x6=1, then α5+α3+α+1α2+1=

A
α2
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B
0
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C
α2
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D
α
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Solution

The correct option is B α2
1+α+...+α5=0 [sum of n roots of unity]
1+α+α3+α5=(α2+α4)
1+α+α3+α5=α2(1+α2)
1+α+α3+α51+α2=α2

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