Question

If $z=x+iy$ is a complex number which satisfies $\frac{|z-5i|}{|z+5i|}=1$, then $z$ lies on

• A. the real axis
• B. the straight line, $y=5$
• C. a circle passing through the origin
• D. the imaginary axis

Answer 1

The correct option is A the real axis

Given : $\frac{|z-5i|}{|z+5i|}=1$
$\Rightarrow |z-5i|=|z+5i|$
So, $z$ is the perpendicular bisector of line segment joning $(0,5)$ and $(0,-5).$
Therefore, the locus of $z$ is $y=0.$
Which is $x-$ axis i.e. real axis.