Let $z$, $w$ be complex numbers such that $\overline{z} +i \overline{w} =0$ and $arg \; zw = \pi$. Then $arg\; z$ equals

Question

( A ) $\frac{\pi}{2}$
( B ) $\frac{5 \pi}{4}$
( C ) $\frac{\pi}{4}$
( D ) $\frac{3 \pi}{4}$