A) a straight line
B) a circle
C) an ellipse
D) a hyperbola
E) none of these
Correct Answer: B
Solution :
Let\[z=x+iy,\]then \[\operatorname{Re}\left( \frac{1}{z} \right)=k\] \[\Rightarrow \] \[\operatorname{Re}\left( \frac{1}{x+iy} \right)=k\] \[\Rightarrow \]\[\operatorname{Re}\left( \frac{x}{{{x}^{2}}+{{y}^{2}}}-\frac{iy}{{{x}^{2}}+{{y}^{2}}} \right)=k\] \[\Rightarrow \] \[k=\frac{x}{{{x}^{2}}+{{y}^{2}}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-\frac{1}{k}x=0\] which is an equation of circle.
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