Let $\;z_{1}\;$ and $\;z_{2}\;$ be two complex numbers such that $\;\overline{z_{1} }+ i\overline{z_{2}}=0\;$ and $\;arg(z_{1} z_{2}) = \pi\;$ . Then find $\;arg(z_{1})$

Question

$(a)\;\large\frac{3 \pi}{2} \qquad(b)\; \large\frac{3 \pi}{4}\qquad(c)\;\large\frac{ \pi}{2}\qquad(d)\;\large\frac{5 \pi}{2}$