A) the x-axis
B) the straight line\[y=5\]
C) a circle passing through the origin
D) None of the above
Correct Answer: A
Solution :
\[\left| \frac{z-5i}{z+5i} \right|=1\] \[\Rightarrow \] \[|z-5i|\,\,=\,\,|z+5i|\] \[\left( \begin{align} & \text{Using}\,\,\text{definition}\,\,|z-{{z}_{1}}|\,\,=\,\,|z-{{z}_{2}}|\,\,\text{gives} \\ & \text{Perpendicular}\,\,\text{bisector}\,\,\text{of}\,\,{{z}_{1}}\,\,and\,\,{{z}_{2}}. \\ \end{align} \right)\] \[\Rightarrow \] Perpendicular bisector of points (0, 5) and (0, -5). which lies on y-axis.You need to login to perform this action.
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