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if `alpha` and `beta` are imaginary cube root of unity then prove `(alpha)^4 + (beta)^4 + (alpha)^-1 . (beta)^-1 = 0`

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Complex cube roots of unity are `omega,omega^(2)`. Let `alpha = omega, beta = omega^(2)`. Thne
`alpha + beta^(2)+ alpha^(-1)beta^(-1)= omega^(4) +(omega^(2))^(4) +(omega^(-1))(omega^(2))^(-1)`
`omega +omega^(2) + omega^(2) + 1=0`
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