If omega is a complex cube root of unity,then | vedclass

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(D) We know that for a complex cube root of unity $\omega$,the following properties hold: $\omega^3 = 1$ and $1 + \omega + \omega^2 = 0$.From $1 + \om

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$4$

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(D) We know that for a complex cube root of unity $\omega$,the following properties hold: $\omega^3 = 1$ and $1 + \omega + \omega^2 = 0$.From $1 + \omega + \omega^2 = 0$,we have $1 + \omega = -\omega^2$ and $1 + \omega^2 = -\omega$.Substituting these into the given expression:$(1 + \omega - \omega^2)(1 - \omega + \omega^2) = (-\omega^2 - \omega^2)(-\omega - \omega)$$= (-2\omega^2)(-2\omega)$$= 4\omega^3$Since $\omega^3 = 1$,the expression simplifies to $4(1) = 4$.

If $\omega$ is a complex cube root of unity,then $(1 + \omega - \omega^2)(1 - \omega + \omega^2) = $

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