Q. If $\omega$ is a cube root of unity, then the value of $\left( 1 - \omega + \omega^{2} \right)^{5} + \left( 1 + \omega - \omega^{2} \right)^{5}$ is
A) 30
B) 32
C) 2
D) None of these
Explanation
(b)
$\left( 1 - \omega + \omega^{2} \right)^{5} + \left( 1 + \omega - \omega^{2} \right)^{5}$
$= ( - 2\omega)^{5} + \left( - 2\omega^{2} \right)^{5}$
$= - 32\omega^{3}\omega^{2} - 32\left( \omega^{3} \right)^{3}\omega$
$= - 32\left( \omega^{2} + \omega \right) = 32$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.