Question

The complex number $z = z + iy$ which satisfies the equation $\left| \frac{z-3i}{z+3i}\right| = 1$, lies on

• A. the X-axis
• B. the straight line y = 3
• C. a circle passing through origin
• D. None of the above

Answer 1

Answer: (A)

the X-axis

Answer 2

$\left| \frac{z-3i}{z+3i}\right| = 1$
$\Rightarrow \left|z-3i\right| = \left|z+3i\right|$
[if $| z-z_1 |=| z + z_2 |$ ,
then it is a perpendicular bisector of $z_1$ and $z_2$]
Hence, perpendicular bisector of $(0, 3)$ and $(0, - 3)$ is X-axis.