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Question

If α and β are imaginary cube roots of unity, then α4+β4+1αβ
[IIT 1977]

A

3

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B
1
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C
2
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Solution

Complex cube root of unity are 1,ω,ω2
Let α=ω,β=ω2; Then α4+β4+α1β1
=ω4+(ω2)4+(ω1)(ω2)1=ω+ω2+1=0.

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