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Question

Let α,β are the imaginary cube roots of unity then find the value of α4.β41α.β.

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Solution

Given α,β are imaginary cube roots of unity.
Then either α=w or, β=w2 and α=w2 or β=w; where w3=1.
In both cases (αβ)=w3=1.
Now, α4β41αβ
=(α/β)41(αβ)
=141/1
=11=0

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