Q. If $\omega$ is an imaginary cube root of unity, then $\left( 1 + \omega - \omega^{2} \right)^{7}$ equals
A) $128\ \omega$
B) $- 128\ \omega$
C) $128\ \omega$
D) $- 128\ \omega^{2}$
Explanation
(d)
We have, $\left( 1 + \omega - \omega^{2} \right)^{7} = \left( - \omega^{2} - \omega^{2} \right)^{7}$
$= ( - 2)^{7}\left( \omega^{2} \right)^{7} = - 128\ \omega^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.