A) Real axis
B) The line \[y=5\]
C) A circle passing through the origin
D) None of these
Correct Answer: A
Solution :
\[\left| \frac{z-5i}{z+5i} \right|=1\]Þ\[\left| \frac{x+i(y-5)}{x+i(y+5)} \right|=1\] Þ \[|x+i(y-5)|\,=\,|x+i(y+5)|\], \[\left( \because \left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|=\frac{|{{z}_{1}}|}{|{{z}_{2}}|} \right)\] Þ \[{{x}^{2}}+25-10y+{{y}^{2}}={{y}^{2}}+{{x}^{2}}+25+10y\] Þ \[20y=0\] Þ \[y=0\].
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