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Q.
The locus of the points representing the complex numbers which satisfy $|z|-2=0,|z-i|-|z+5 i|=0$ is:
Complex Numbers and Quadratic Equations
Solution:
$|z-i|=|z+5 i|$ 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 $(0,-2)$.