If omega is an imaginary cube root of unity,( | vedclass

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(D) We know that $1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$.Substituting this into the expression:$(1 + \omega - \omega^2)^7 =

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$-128\omega^2$

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(D) We know that $1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$.Substituting this into the expression:$(1 + \omega - \omega^2)^7 = (-\omega^2 - \omega^2)^7$$= (-2\omega^2)^7$$= (-2)^7 	imes (\omega^2)^7$$= -128 	imes \omega^{14}$Since $\omega^3 = 1$,we have $\omega^{14} = (\omega^3)^4 	imes \omega^2 = 1^4 	imes \omega^2 = \omega^2$.Therefore,the expression equals $-128\omega^2$.

If $\omega$ is an imaginary cube root of unity,$(1 + \omega - \omega^2)^7$ equals

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