Mathematics - Complex Number Question with Solution | TestHub

$|z\omega |=1$
$$\text{ As, }\mathrm{Arg}\left(\frac{z}{\omega }\right)=\frac{\pi }{2}\text{ therefore }\frac{z}{\omega }=i$$ $\therefore \left|\frac{z}{\omega }\right|=1$
From (1) \& (2), $|z|=|\omega |=1$ and $\frac{z}{\omega }+\frac{\bar{z}}{\omega }=0;z\bar{\omega }+\bar{z}\omega =0$ $\bar{z}\omega =-z\bar{\omega }=\frac{-z}{\omega }\cdot \bar{\omega }\cdot \omega ;\bar{z}\omega =-i|\omega {|}^2=-\mathrm{i}$