Complex Numbers And Quadratic Equations question 91
Question: The amplitude of $ \frac{1+\sqrt{3}i}{\sqrt{3}+1} $ is [Karnataka CET 1992; Pb CET 2001]
Options:
A) $ \frac{\pi }{3} $
B) $ -\frac{\pi }{3} $
C) $ \frac{\pi }{6} $
D) $ -\frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ z=\frac{1+i\sqrt{3}}{1+\sqrt{3}}\therefore amp(z)orarg(z) $ $ ={{\tan }^{-1}}[ \frac{\sqrt{3}/(1+\sqrt{3})}{1/(1+\sqrt{3})} ]={{\tan }^{-1}}\sqrt{3}=\frac{\pi }{3} $
BETA
