Complex Numbers And Quadratic Equations question 114
Question: The amplitude of $ \frac{1+\sqrt{3}i}{\sqrt{3}-i} $ is [RPET 2001]
Options:
A) 0
B) $ \pi /6 $
C) $ \pi /3 $
D) $ \pi /2 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ z=\frac{1+\sqrt{3}i}{\sqrt{3}-i} $ $ =\frac{1+\sqrt{3}i}{\sqrt{3}-i}\times $ $ \frac{\sqrt{3}+i}{\sqrt{3}+i} $ $ =\frac{\sqrt{3}+i+3i-\sqrt{3}}{3+1} $ = $ \frac{4i}{4}=i $ amp $ (z)=\pi /2 $ $ [\because \tan \theta =b/a] $
BETA
