Complex Numbers And Quadratic Equations question 86
Question: If $ \bar{z} $ be the conjugate of the complex number $ z $ , then which of the following relations is false [MP PET 1987]
Options:
A) $ |z|=|\bar{z}| $
B) $ z.\bar{z}=|\bar{z}{{|}^{2}} $
C) $ \overline{z_1+z_2}=\overline{z_1}+\overline{z_2} $
D) $ argz=arg\bar{z} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ z=x+iy,\overline{z}=x-iy $ Since $ arg(z)=\theta ={{\tan }^{-1}}\frac{y}{x} $ $ arg(\overline{z})=\theta ={{\tan }^{-1}}( \frac{-y}{x} ) $ Thus $ arg(z)\ne arg(\overline{z}) $ .
BETA
