(d) $|z|\,|\omega |\, = 1$ ……$(i)$
and $arg\,\left( {\frac{z}{\omega }} \right) = \frac{\pi }{2}\,\,\, \Rightarrow \,\,\frac{z}{\omega } = i$ $⇒$  $\left| {\frac{z}{\omega }} \right| = 1$ …..$(ii)$
From equation $(i) $ and $(ii)$
$|z|\, = \,|\omega |\, = 1$ and $\frac{z}{\omega } + \frac{{\bar z}}{{\bar \omega }} = 0;\,\,\,z\bar \omega + \bar z\omega = 0$
$\bar z\omega = – z\bar \omega = \frac{{ – z}}{\omega }\bar \omega \,\omega $; $\bar z\omega = – \,i\,|\omega {|^2} = – i.$.