Q. The value of $\left( - \frac{1}{2} + \frac{\sqrt{3}i}{2} \right)^{1000}$ is
A) $\omega^{3}$
B) $\omega^{2}$
C) $\omega^{3} - \omega$
D) $\omega$
Explanation
(d)
We know, $\omega = \frac{- 1 + \sqrt{3}i}{2}$
$\therefore\ \ \ \ \ \left( - \frac{1}{2} + \frac{\sqrt{3}i}{2} \right)^{1000} = (\omega)^{1000} = \omega\ \ \ \ \ \ \lbrack\because\omega^{3} = 1\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.