If $\omega$ is complex cube root of unity and $(1+\omega)^7=\mathrm{A}+\mathrm{B} \omega$, then values of A and B are, respectively.

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Aicharya · Accepted Answer

$\begin{aligned} & (1+\omega)^7=\mathrm{A}+\mathrm{B} \omega \ & 	herefore \mathrm{A}+\mathrm{B} \omega=\left(-\omega^2ight)^7 \quad \ldots\left(\because 1+\omega+\omega^2=0ight] \ & =(-1) \omega^{14}=-\omega^{12} \omega^2=-\omega^2=(1+\omega) \ & 	herefore A=1, B=1\end{aligned}$

If $\omega$ is complex cube root of unity and $(1+\omega)^7=\mathrm{A}+\mathrm{B} \omega$, then values of A…

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