Q49 / 120 · VITEEE 2016 · Mathematics
The value of $\left(1+\omega-\omega^{2}\right)^{7}$ is
- A$128 \omega^{2}$
- Correct answerB$-128 \omega^{2}$
- C$128 \omega$
- D$-128 \omega$
Solution
$\begin{aligned} &\left(1+\omega-\omega^{2}\right)^{7}=\left(-\omega^{2}-\omega^{2}\right)^{7}=\left(-2 \omega^{2}\right)^{7} \\ &=-128\left(\omega^{4}\right)^{3} \omega^{2}=-128 \omega^{2} \end{aligned}$
Hence, the correct answer is option: 'B'.