Question

The complex number $z=x+iy$ which satisfy the equation $\left|\frac{z-5i}{z+5i}\right|=1$, lie on

• A. the x-axis
• B. the straight line y=5
• C. a circle passing through the origin
• D. None of the above

Answer 1

Answer: (A)

$|\frac{z-5i}{z+5i}|=1$
$\Rightarrow |z-5i|=|z+5i|$
(Using definition $\left|z-z_1\right|=\left|z-z_2\right|$ gives Perpendicular bisector of $z_1$ and $z_2$)

$\Rightarrow$ Perpendicular bisector of points $(0,5)$
and $(0,-5)$ which lies on $y$ -axis.