Locus of a point $z$ in argand plane satisfying $|z^2-(\overline{z}{)}^2|=|z{|}^2,Re(z)\ge 0,Im(z)\ge 0$ is :

The correct option is B Pair of straight line
$\begin{array}{c}\left|z^2-{\left(\overline{z}\right)}^2\right|={\left|z\right|}^2\\ Re\left(z\right)\ge 0,Im\left(z\right)\ge 0\\ \left|\left(z-\overline{z}\right)\left(z+\overline{z}\right)\right|={\left|z\right|}^2\\ 4xy=x^2+y^2\\ x^2+y^2-4xy=0\\ \Rightarrow Pairofstraightlines\end{array}$

Hence,

Option$B$ is correct answer.