Mathematics - Complex Number Question with Solution | TestHub

${\left|z^2-1\right|}^2=\left(|z{|}^2+1\right)\Rightarrow \left(z^2-1\right)\left({\bar{z}}^2-1\right)=|z{|}^4+2|z{|}^2+1$ $\Rightarrow z^2+{\bar{z}}^2+2z\bar{z}=0\Rightarrow z+\bar{z}=0$ $\Rightarrow R(z)=0\Rightarrow z$ lies on the imaginary axis.