Question

POQis a straight line through the origin O,P and Q represent the complex numbers a+ib andc+id respectively and OP=OQ, then

• A. |a+ib|=|c+id|
• B. a+c=b+d
• C. arg(a+ib)=arg(c+id)
• D. None of these

Answer 1

The correct option is B

a+c=b+d

(a,b) It is given that OP=OQ

$\therefore$ |$\overline{OP}$|=|$\overline{OQ}$| $\Rightarrow$ |a+ib|=|c+id|

Also $\overline{OP}$ =-$\overline{OQ}$,$\therefore$ $\overline{OP}$ + $\overline{OQ}$=0

$\Rightarrow$ (a+c)+i(b+d) =0 $\Rightarrow$ a+c=0=b+d