• # question_answer 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

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