Search any question & find its solution
Question:
Answered & Verified by Expert
Amplitude of $\frac{1+\sqrt{3} \mathrm{i}}{\sqrt{3}+1}$ is :
Options:
Solution:
2846 Upvotes
Verified Answer
The correct answer is:
$\frac{\pi}{3}$
$\operatorname{Let} r(\cos \theta+i \sin \theta)$
$=\frac{1+i \sqrt{3}}{\sqrt{3}+1}=\frac{1}{\sqrt{3}+1}+i \frac{\sqrt{3}}{\sqrt{3}+1}$
$\Rightarrow r \cos \theta=\frac{1}{\sqrt{3}+1} ; r \sin \theta=\frac{\sqrt{3}}{\sqrt{3}+1}$
$=\frac{1+i \sqrt{3}}{\sqrt{3}+1}=\frac{1}{\sqrt{3}+1}+i \frac{\sqrt{3}}{\sqrt{3}+1}$
$\Rightarrow r \cos \theta=\frac{1}{\sqrt{3}+1} ; r \sin \theta=\frac{\sqrt{3}}{\sqrt{3}+1}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.