1. Tardigrade
  2. Question
  3. Mathematics
  4. The complex number z=x+i y which satisfy the equation |(z-5 i/z+5 i)|=1, lie on

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

ManipalManipal 2012

Solution:

$|\frac{z-5 i}{z+5 i}|=1$
$\Rightarrow | z-5 i|=| z+5 i |$
(Using definition $\left| z-z_{1}\right|=\left| z-z_{2}\right|$ gives Perpendicular bisector of $z_{1}$ and $z_{2}$)
image
$\Rightarrow $ Perpendicular bisector of points $(0,5)$
and $(0,-5)$ which lies on $y$ -axis.