If $z\neq 0$ is a complex no having arg=$\large\frac{\pi}{4}$,then

Question

$\begin{array}{1 1}(A)Re (z^2)=0 \\ (B) Im(z^2)=0 \\ (C) Re(z^2)=Im(z^2) \\(D) None\;of\;these \end{array}$