Question

The equation $|z-1{|}^2+|z+1{|}^2=2$ represents

• A. a circle of radius ' 1 '
• B. a straight line
• C. the ordered pair $(0,0)$
• D. set of two points

Answer 1

Answer: (C)

$|z-1{|}^2+|z+1{|}^2=2$
$z\bar{z}+1-(z+\bar{z})+z\bar{z}+1+(z+\bar{z})=2$
$\Rightarrow z\bar{z}=0$
$\Rightarrow z=0$