Let $z,\omega$ be two comlex numbers such that $\overline{z}+i\overline{\omega}=0$ and $arg(z\omega)=\pi$, then $arg(z)$ equal to

Question

$\begin{array}{1 1}(A)\large\frac{\pi}{4} \\ (B) \large\frac{\pi}{2} \\ (C) \large\frac{3 \pi}{4}\\(D) \large\frac{5 \pi}{4} \end{array}$