Search any question & find its solution
Question:
Answered & Verified by Expert
If $\omega$ is a cube root of unity, then the value of $\left(1-\omega+\omega^2\right)^5+\left(1+\omega-\omega^2\right)^5=$
Options:
Solution:
2173 Upvotes
Verified Answer
The correct answer is:
$32$
$\begin{aligned} & \left(1-\omega+\omega^2\right)^5+\left(1+\omega-\omega^2\right)^5 \\ & =(-2 \omega)^5+\left(-2 \omega^2\right)^5=-32 \omega^3 \omega^2-32\left(\omega^3\right)^3 \omega \\ & =-32\left(\omega^2+\omega\right)=-32(-1)=32\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.