If omega (neq 1) is a cube root of unity and | vedclass

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(C) We know that for the cube roots of unity,$1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$.Substituting this into the given expre

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$1, 1$

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(C) We know that for the cube roots of unity,$1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$.Substituting this into the given expression:$(1 + \omega)^7 = (-\omega^2)^7$$= -\omega^{14}$Since $\omega^3 = 1$,we have $\omega^{14} = \omega^{12} \cdot \omega^2 = (\omega^3)^4 \cdot \omega^2 = 1^4 \cdot \omega^2 = \omega^2$.Thus,$(1 + \omega)^7 = -\omega^2$.Using the identity $1 + \omega + \omega^2 = 0$,we get $-\omega^2 = 1 + \omega$.Comparing $1 + \omega$ with $A + B\omega$,we get $A = 1$ and $B = 1$.

If $\omega (\neq 1)$ is a cube root of unity and $(1 + \omega)^7 = A + B\omega$,then $A$ and $B$ are equal to:

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