Q. Which of the following is a fourth root of$\frac{1}{2} + i\frac{\sqrt{3}}{2}$?
A) $cis\frac{\pi}{12}$
B) $cis\frac{\pi}{2}$
C) $cis\frac{\pi}{6}$
D) $cis\frac{\pi}{3}$
Explanation
(a)
$\left( \frac{1}{2} + \frac{i\sqrt{3}}{2} \right)^{1/4} = \left( \cos{\frac{\pi}{3} + i\sin\frac{\pi}{3}} \right)^{1/4}$
$= \cos{\frac{\pi}{12} + i\sin\frac{\pi}{12}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.