Complex Numbers And Quadratic Equations question 111
Question: The amplitude of $ \frac{1+\sqrt{3}i}{\sqrt{3}+i} $ is [DCE 1999; Karnataka CET 2005]
Options:
A) $ \frac{\pi }{6} $
B) $ -\frac{\pi }{6} $
C) $ \frac{\pi }{3} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ amp( \frac{1+\sqrt{3}i}{\sqrt{3}+i} ) $ $ =amp(1+\sqrt{3}i)-amp(\sqrt{3}+i) $ $ =\frac{\pi }{3}-\frac{\pi }{6}=\frac{\pi }{6} $ .
BETA
