A) lies on real axis
B) lies on imaginary axis
C) lies on a circle
D) lies on an ellipse
Correct Answer: B
Solution :
Given, \[|{{z}^{2}}-1|=|z{{|}^{2}}+1\] \[\Rightarrow \] \[|{{z}^{2}}-1|=|z{{|}^{2}}+|-1|\] From the above it is clear that origin,\[-1\]and \[{{z}^{2}}\]lies on the same line and\[{{z}^{2}}\]and\[-1\] lies on the same side of origin. So,\[{{z}^{2}}\]is a negative number. So, z is purely imaginary. Hence, z lies on y-axis.
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