A) The parabola \[{{x}^{2}}+{{y}^{2}}=1\]
B) The hyperbola \[{{x}^{2}}-{{y}^{2}}=1\]
C) Parabola or a circle
D) All the above
Correct Answer: B
Solution :
\[z=(x+iy)\]Þ \[{{z}^{2}}={{x}^{2}}-{{y}^{2}}+2ixy\] Þ \[\operatorname{Re}({{z}^{2}})=1\]Þ \[{{x}^{2}}-{{y}^{2}}=1\], which is a hyperbola.
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