Complex Numbers And Quadratic Equations question 625
Question: If z and $ \omega $ are two non-zero complex numbers such that $ | z\omega |=1 $ and $ Arg(z)-Arg(\omega )=\frac{\pi }{2}, $ then $ \bar{z}\omega $ is equal to
Options:
A) $ -i $
B) $ 1 $
C) $ -1 $
D) $ i $
Show Answer
Answer:
Correct Answer: C
Solution:
Consider $ |\bar{z}\omega ||\bar{z}||\omega |=|z||\omega |=|z\omega |=1 $ Consider $ Arg(\bar{z}\omega )=\arg (\bar{z})+arg(\omega )=-arg(z)+arg\omega $ $ =-\frac{\pi }{2}\therefore \bar{z}\omega =-1 $
BETA
