Complex Numbers And Quadratic Equations question 115
Question: If $ z=\frac{-2}{1+\sqrt{3}i} $ then the value of $ arg(z) $ is [ Orissa JEE 2002]
Options:
A) $ \pi $
B) $ \pi /3 $
C) $ 2\pi /3 $
D) $ \pi /4 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ z=\frac{-2}{1+\sqrt{3}i} $ = $ \frac{-2}{1+\sqrt{3}i}\times \frac{1-\sqrt{3}i}{1-\sqrt{3}i} $ $ =\frac{-2+2\sqrt{3}i}{1+3} $
$ \Rightarrow z=\frac{-1}{2}+\frac{\sqrt{3}}{2}i $
$ \Rightarrow arg(z)={{\tan }^{-1}}( -\frac{\sqrt{3}/2}{1/2} )=\frac{2\pi }{3} $ .
BETA
