If $z,\omega$ are complex numbers such that $\overline z+i\omega=0$, then the $arg \:z=?$

Question

$\begin{array}{1 1}(A) \;\large\frac{\pi}{6}\\(B)\;-\large\frac{\pi}{6}\\(C)\;\large\frac{\pi}{3}\\(D)\;-\large\frac{\pi}{3}\end{array}$