Q. The amplitude of $\frac{1 + i\sqrt{3}}{\sqrt{3} + i}$ is
A) $\frac{\pi}{3}$
B) $\frac{\pi}{4}$
C) $\frac{2\pi}{3}$
D) $\frac{\pi}{6}$
Explanation
(d)
Let $z = \frac{1 - i\sqrt{3}}{\sqrt{3} + i} = \frac{1 + i\sqrt{3}}{(\sqrt{3} + i)} \times \frac{(\sqrt{3} - i)}{(\sqrt{3} - i)} = \frac{\sqrt{3} + i}{2}$
$\therefore\ \ \ amp\ (z) = \tan^{- 1}\left( \frac{1}{\sqrt{3}} \right) = \frac{\pi}{6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.