IIT-JEE 1981Question 1
The complex numbers $z=x+iy$ which satisfy the equation $\left|\dfrac{z-5i}{z+5i}\right|=1$ lie on
Complex Numbers
Solution
$|z-5i|=|z+5i|$: $z$ is equidistant from $5i$ and $-5i$, so it lies on their perpendicular bisector $y=0$, the $x$-axis.