A) \[z\]lies on \[x\]-axis
B) \[z\]lies on \[y\]-axis
C) z lies on a circle
D) None of these
Correct Answer: C
Solution :
Here \[|z-zi|=1\Rightarrow |x+iy-i(x+iy)|=1\] Þ \[|(x+y)+i(y-x)|=1\]Þ \[2{{x}^{2}}{{y}^{2}}=2{{x}^{2}}{{y}^{2}}+4{{x}^{2}}\] Þ \[2({{x}^{2}}+{{y}^{2}})=1\]. Hence z lies on a circle.
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