A) \[z=0\]
B) \[\operatorname{Re}(z)=0\]
C) \[\operatorname{Im}\,(z)=0\]
D) None of these
Correct Answer: A
Solution :
Let \[z=x+iy,\overline{z}=x-iy\] \[\therefore \] \[z\overline{z}=0\] Þ \[(x+iy)(x-iy)=0\]Þ \[{{x}^{2}}+{{y}^{2}}=0\] It is possible only when \[x\] and \[y\]both simultaneously zero i.e., \[z=0+0i=0\]
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