If α is a non real root of z=(1)1/5, then the value of (1+α+α2+α−2−α−1) 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+1α2−1α ⇒E=α2+α3+α4+1−αα2 ⇒E=(1+α+α2+α3+α4)−2αα2 We know that, sum of n roots of unity is zero, so ⇒E=0−2αα2=−2α ⇒E=−2α4