Complex Numbers And Quadratic Equations question 321
Question: $ POQ $ is a straight line through the origin $ O,P $ and $ Q $ represent the complex numbers $ a+ib $ and $ c+id $ respectively and $ OP=OQ $ , then
Options:
A) $ |a+ib|=|c+id| $
B) $ a+c=b+d $
C) $ arg(a+ib)=arg(c+id) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
It is given that $ OP=OQ $
$ \therefore |\overrightarrow{OP}|=|\overrightarrow{OQ}| $
Þ $ |a+ib|=|c+id| $ Also $ \overrightarrow{OP}=-\overrightarrow{OQ},\therefore \overrightarrow{OP}+\overrightarrow{OQ}=0 $
Þ $ (a+c)+i(b+d)=0 $
Þ $ a+c=0=b+d $
BETA
