Complex Numbers And Quadratic Equations question 120
The sum of amplitudes of z and another complex number is $ \pi $. The other complex number can be written[Orissa JEE 2004]
Options:
A) $ \bar{z} $
B) $ -\overline{z} $
z
D) $ -z $
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ z=x+iy $ and let their complex $ z_2 $ and given that $ arg\ (z)+z_2=\pi $ $ z_2=\pi -arg(z) $ ; $ z_2=\pi +[ -{{\tan }^{-1}}\frac{y}{x} ] $ $ z_2=\pi +[arg\ (\bar{z})] $ which lies in second quadrant, i.e. $ \bar{z} $ .
BETA
