Let z and w be complex numbers such that $\stackrel{-}{z}+i\stackrel{-}{\omega }=0$ and $\arg \left(z\omega \right)=\pi$, then arg z=

$\begin{array}{l}\overline{z}=-i\overline{\omega }\Rightarrow z=i\omega \\ \Rightarrow \text{ arg }z=\arg i+\arg \omega =\frac{\pi }{2}+\arg \omega \end{array}$

But $\arg \left(z\omega \right)=\pi \Rightarrow \arg \omega =\pi -\arg z$

Now, $\arg z=\frac{\pi }{2}+\arg \omega$

$\arg z=\pi =a\mathrm{rg}\omega$

Adding (i) and (ii), $2\arg z=\frac{3\pi }{2},\arg z=\frac{3\pi }{4}$