The mirror image of the curve  $arg\left(\frac{z+i}{z-1}\right)=\frac{\pi }{4}(i=\sqrt{-1})$ in the line $x-y=0$ is

The image of  z in the line $y=xisi\stackrel{-}{z}.$

The image of the given curve is

arg $\left(\frac{i\overline{z}+i}{i\stackrel{-}{z}-1}\right)=\frac{\pi }{4}$

arg $\left(\frac{\overline{z}+1}{\stackrel{-}{z}+i}\right)=\frac{\pi }{4}$

- arg  $\left(\frac{z+1}{z-i}\right)=\frac{\pi }{4}$       $[\therefore \arg (\stackrel{ }{\stackrel{-}{z})=-\arg (z)}]$

$\arg \left(\frac{z-i}{z+1}\right)=\frac{\pi }{4}$             $[\therefore \arg \left(\frac{z_1}{z_2}\right)=-\arg \left(\frac{z_2}{z_1}\right)]$