If $\omega$ is acomplex cube root of unity, then the value of $\sin\left\{ \left( \omega^{10} + \omega^{23} \right)\pi - \frac{\pi}{6} \right\}$ is

Question

Dr. Abubacker · Accepted Answer

(d)
Since, $\omega$ is a complex cube root of unity
Now, $\omega^{10} + \omega^{23} = \left( \omega^{3} ight)^{3}\omega + \left( \omega^{3} ight)^{7}\omega^{2}$
$= \omega + \omega^{2} = - 1$
$	herefore\ \ \sin\left\{ \left( \omega^{10} + \omega^{23} ight)\pi - \frac{\pi}{6} ight\} = \sin\left( - \pi - \frac{\pi}{6} ight) = \sin{\frac{\pi}{6} = \frac{1}{2}}$

Q. If $\omega$ is acomplex cube root of unity, then the value of $\sin\left\{ \left( \omega^{10} + \omega^{23} \right)\pi - \frac{\pi}{6} \right\}$ is

Explanation

Reviewed by Dr. Abubacker

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