Let $z$  and $\omega$ be a complex numbers such that $\overline{z}+i\overline{w}=0$ and $zw=\text{π}$ ,then

$\arg \left(z\right)$  equals =

 

$\begin{array}{c}\arg \left(zw\right)=\text{π}\\ \Rightarrow \arg z+\arg w=\text{π}\to \left(1\right)\end{array}$ 

$\begin{array}{c}\overline{z}+i\overline{w}=0\\ \Rightarrow \overline{z}=-i\overline{w}\end{array}$

$\Rightarrow \overline{\overline{z }}=i \overline{ \overline{w}}$

$\begin{array}{c}\therefore z=iw\\ \\ \Rightarrow \arg z=arg iw=arg i +arg w =\frac{\text{π}}{2}+\arg w\end{array}$            

$\Rightarrow \arg z=\frac{\text{π}}{2}+\text{π}-\arg z$        [from (1)]

   $\therefore \arg z=\frac{3\text{π}}{4}$