Question

The amplitude of $\frac{1+i \sqrt{3}}{\sqrt[1]{3}+i}$ is

(A) $\frac{\pi}{6}$

(B) $\frac{\pi}{4}$

(C) $\frac{\pi}{3}$

(D) None of these

Answer 1

$\text { Let }  z=\frac{1+i \sqrt{3}}{\sqrt{3}+i} \times \frac{\sqrt{3}-i}{\sqrt{3}-i}=\frac{\sqrt{3}+i}{2} \\$

$\therefore \quad \theta=\tan ^{-1}\left(\frac{1 / 2}{\sqrt{3} / 2}\right)=\frac{\pi}{6}$

So, The correct option will be (A).