If 1, omega, omega^{2} are three cube roots o | vedclass

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(D) We have,$(1-\omega+\omega^{2})(1+\omega-\omega^{2}) \quad \dots(1)$ We know that,$1+\omega+\omega^{2}=0$. From this,we can write: $1+\omega^{2} =

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$4$

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(D) We have,$(1-\omega+\omega^{2})(1+\omega-\omega^{2}) \quad \dots(1)$ We know that,$1+\omega+\omega^{2}=0$. From this,we can write: $1+\omega^{2} = -\omega$,so $(1-\omega+\omega^{2}) = -\omega - \omega = -2\omega$. $1+\omega = -\omega^{2}$,so $(1+\omega-\omega^{2}) = -\omega^{2} - \omega^{2} = -2\omega^{2}$. Substituting these values into Eq. $(1)$: $(-2\omega)(-2\omega^{2}) = 4\omega^{3}$. Since $\omega^{3}=1$,the expression becomes $4(1) = 4$.

If $1, \omega, \omega^{2}$ are three cube roots of unity,then $(1-\omega+\omega^{2})(1+\omega-\omega^{2})$ is

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