If $1, \omega, \omega^2$ denote the cube roots of unity, then the value of $\left(1-\omega+\omega^2\right)^5+\left(1+\omega-\omega^2\right)^5$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 1+\omega+\omega^2=0 \ & \left(1-\omega+\omega^2ight)^5+\left(1+\omega-\omega^2ight)^5 \ & =(-2 \omega)^5+\left(-2 \omega^2ight)^5 \ & =-32\left(\omega^5+\omega^{10}ight)=-32\left(\omega^2+\omegaight)=32\end{aligned}$

If $1, \omega, \omega^2$ denote the cube roots of unity, then the value of…

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