A) \[\operatorname{Re}(z)=0\Rightarrow \operatorname{Im}({{z}^{2}})=0\]
B) \[\operatorname{Re}({{z}^{2}})=0\Rightarrow \operatorname{Im}({{z}^{2}})=0\]
C) \[\operatorname{Re}(z)=0\Rightarrow \operatorname{Re}({{z}^{2}})=0\]
D) None of these
Correct Answer: A
Solution :
If \[z\ne 0\]. Let \[z=x+iy\] Þ \[{{z}^{2}}={{x}^{2}}-{{y}^{2}}+i(2xy)\] Re(z)= 0 Þ \[x=0\]. Therefore \[\operatorname{Im}({{z}^{2}})=2xy=0\] Thus \[\operatorname{Re}(z)=0\Rightarrow \operatorname{Im}({{z}^{2}})=0\].
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