Q. If $z = r{(cos}{\theta + i\sin\theta})$, then the value of $\frac{z}{\overline{z}} + \frac{\overline{z}}{z}$ is
A) $\cos{2\theta}$
B) ${2cos}{2\theta}$
C) ${2cos}\theta$
D) ${2sin}\theta$
Explanation
(b)
$\frac{z}{\overline{z}} + \frac{\overline{z}}{z} = \frac{re^{i\theta}}{re^{- i\theta}} + \frac{re^{- i\theta}}{re^{i\theta}} = e^{i2\theta} + e^{- i2\theta} = 2\cos{2\theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.