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Question

If α and β are the complex cube-roots of unity, then α4+β4+α1β1=

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Solution

The correct option is A 0
Cube roots of unity are 1, ω and ω2
where ω and ω2 are non-real complex cube roots of unity.

Now, the properties of cube roots of unity are:
1+ω+ω2=0 and ω3=1

If α=ω and β=ω2
then
α4+β4+α1β1=ω4+(ω2)4+1ωω2
=ω4+ω8+1ω3
=ω3ω+(ω3)2ω2+1
=ω+ω2+1
=0






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