If $z$ and $\omega$ are two non-zero complex numbers such that $|z \; \omega| = 1$, and $arg (z) - arg(\omega) = \frac{\pi}{2}$, then $\overline{z} \omega$ is equal to :

Question

( A ) $1$
( B ) $i$
( C ) $-i$
( D ) $-1$