Complex Numbers And Quadratic Equations question 113
Question: If $ argz<0 $ then $ arg(-z)-arg(z) $ is equal to [IIT Screening 2000]
Options:
A) $ \pi $
B) $ -\pi $
C) $ -\frac{\pi }{2} $
D) $ \frac{\pi }{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
Since arg $ z<0 $ i.e. - ve, we choose arg z = - q where $ \theta $ is $ {{( \frac{1-z}{1-\frac{1}{z}} )}^{10}} $ arg $ (-z)=-[+\pi -(-\theta )] $ $ =-\pi -\theta =2\pi +(-\pi -\theta )=\pi +arg(z) $
$ \Rightarrow arg(-z)-arg(z)=\pi . $
BETA
