Question

The locus of the points representing the complex numbers which satisfy $|z|-2=0,|z-i|-|z+5i|=0$ is:

• A. a circle with centre at origin
• B. a straight line passing through origin
• C. the single point $(0,-2)$
• D. None of these

Answer 1

Answer: (C)

$|z-i|=|z+5i|$ represents equation of perpendicular bisector of points $(0,1)$ and $(0,-5)$
i.e., $y=-2$,
now $|z|=2$ is $x^2+$ $y^2=4$
$\Rightarrow x^2+4=4$
$\Rightarrow x=0$
$\therefore z$ represents a single point $(0,-2)$.