If $\omega$ is an imaginary cube roots of unity, then $\left(1+\omega-\omega^{2}\right)^{7}$ equals\

Question

If $\omega$ is an imaginary cube roots of unity, then $\left(1+\omega-\omega^{2}ight)^{7}$ equals\

Professor PC Thomas Classes · Answer

(d) : $\left(1+\omega-\omega^{2}ight)^{7}=\left(-\omega^{2}-\omega^{2}ight)^{7}$\ $=(-2)^{7}\left(\omega^{2}ight)^{7}=-128 \omega^{14}=-128 \omega^{2}$\