Question

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+i}$is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. 0
• D. $\frac{\pi }{6}$

Answer 1

The correct option is D $\frac{\pi }{6}$

$Z=\frac{1+\sqrt{3}i}{\sqrt{3}+i}$
$\Rightarrow \left(\frac{1+\sqrt{3}i}{\sqrt{3}+i}\right)\left(\frac{\sqrt{3}-i}{\sqrt{3}-i}\right)=\frac{2\sqrt{3}+2i}{4}$
$\therefore$ Amplitude of $Z$ is ${\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)=\frac{\pi }{6}$
Hence, option D.