If $\omega$ is an imaginary cube root of unity then the value of $\sin \left\{\left(\omega^{10}+\ome

Question

If $\omega$ is an imaginary cube root of unity then the value of $\sin \left\{\left(\omega^{10}+\omega^{23}ight) \pi-\frac{\pi}{4}ight\}$ is\

Professor PC Thomas Classes · Answer

(c) : $\sin \left\{\left(\omega^{10}+\omega^{23}ight) \pi-\frac{\pi}{4}ight\}$\ $=\sin \left\{\left(\omega+\omega^{2}ight) \pi-\frac{\pi}{4}ight\}$\ $=\sin \left(-\pi-\frac{\pi}{4}ight)=-\sin \left(\pi+\frac{\pi}{4}ight)=\sin \frac{\pi}{4}=\frac{1}{\sqrt{2}}$.\