A) \[\operatorname{Re}(z)<2\]
B) \[\operatorname{Re}(z)>0\]
C) \[\operatorname{Re}(z)=0\]
D) z lies on \[x=-\frac{1}{2}\]
Correct Answer: D
Solution :
\[{{\operatorname{z}}^{n}}={{(z+1)}^{n}}\,\,\Rightarrow {{\left| z \right|}^{n}}\,=\,\,{{\left| z+1 \right|}^{n}}\] or \[\left| z \right|=\left| z+1 \right|\] So the distance of point z remain same from (0, 0) and(-1, 0). So, z lies on perpendicular bisector of line joining (0, 0) and (-1, 0) that is on \[\operatorname{x} = -\frac{1}{2}\]
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