If 1, omega, omega^2 are the cube roots of un | vedclass

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(D) We know that $1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$ and $1 + \omega^2 = -\omega$. Substituting these values into the e

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(D) We know that $1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$ and $1 + \omega^2 = -\omega$. Substituting these values into the expression: $\omega^2(1 + \omega)^3 - (1 + \omega^2)\omega = \omega^2(-\omega^2)^3 - (-\omega)\omega$ $= \omega^2(-\omega^6) + \omega^2$ $= -\omega^8 + \omega^2$ Since $\omega^3 = 1$,we have $\omega^8 = \omega^6 	imes \omega^2 = 1 	imes \omega^2 = \omega^2$. Thus,$-\omega^2 + \omega^2 = 0$.

If $1, \omega, \omega^2$ are the cube roots of unity,then $\omega^2(1 + \omega)^3 - (1 + \omega^2)\omega = $

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