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(B) The imaginary cube roots of unity are $\omega$ and $\omega^2$.Let $\alpha = \omega$ and $\beta = \omega^2$.We know that $\omega^3 = 1$ and $1 + \o

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(B) The imaginary cube roots of unity are $\omega$ and $\omega^2$.Let $\alpha = \omega$ and $\beta = \omega^2$.We know that $\omega^3 = 1$ and $1 + \omega + \omega^2 = 0$.Substituting these values into the expression $\alpha^4 + \beta^4 + \frac{1}{\alpha\beta}$:$= \omega^4 + (\omega^2)^4 + \frac{1}{\omega \cdot \omega^2}$$= \omega^4 + \omega^8 + \frac{1}{\omega^3}$$= \omega + \omega^2 + \frac{1}{1}$$= \omega + \omega^2 + 1$$= 0$.

If $\alpha$ and $\beta$ are imaginary cube roots of unity,then $\alpha^4 + \beta^4 + \frac{1}{\alpha\beta} = $

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