Complex Numbers And Quadratic Equations question 107
Question: If $ |z_1|=|z_2| $ and $ ampz_1+ampz_2=0 $ , then [MP PET 1999]
Options:
A) $ z_1=z_2 $
B) $ {{\bar{z}}_1}=z_2 $
C) $ z_1+z_2=0 $
D) $ {{\bar{z}}_1}={{\bar{z}}_2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ z_1=r_1(\cos {\theta_1}+i\sin {\theta_1}) $ Then $ |z_1|=|z_2|\Rightarrow |z_2|=r_1 $ and $ arg(z_1)+arg(z_2)=0 $ Þ $ arg(z_2)=-arg(z_1)=-{\theta_1} $ $ z_2=r_1[\cos (-{\theta_1})-i\sin (-{\theta_1})]=r_1(\cos {\theta_1}-i\sin {\theta_1}) $ $ ={{\bar{z}}_1} $ $ {{\bar{z}}_1}=z_2 $ .
BETA
