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

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(C) We know that $1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$.Substituting this into the given equation:$(1 + \omega)^7 = A + B\

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$1, 1$

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(C) We know that $1 + \omega + \omega^2 = 0$,which implies $1 + \omega = -\omega^2$.Substituting this into the given equation:$(1 + \omega)^7 = A + B\omega$$(-\omega^2)^7 = A + B\omega$$-\omega^{14} = A + B\omega$Since $\omega^3 = 1$,we have $\omega^{14} = (\omega^3)^4 \cdot \omega^2 = 1^4 \cdot \omega^2 = \omega^2$.So,$-\omega^2 = A + B\omega$.Using $1 + \omega + \omega^2 = 0$,we get $\omega^2 = -1 - \omega$.Therefore,$-(-1 - \omega) = A + B\omega$.$1 + \omega = A + B\omega$.Comparing the coefficients,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 respectively,the numbers

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