Thank you for reporting, we will resolve it shortly
Q.
The mirror image of the curve $\arg \left(\frac{z-3}{z-i}\right)=\frac{\pi}{6}$ in the real axis is
Complex Numbers and Quadratic Equations
Solution:
The image of $z$ in the real axis is $\bar{z}$
$\therefore$ The image of given curve is given by $\arg \left(\frac{\bar{z}-3}{\bar{z}-i}\right)=\frac{\pi}{6}$
But $\arg \bar{z}=-\arg z$
$\therefore \arg \left(\frac{\bar{z}-3}{\bar{z}-i}\right)=\frac{\pi}{6}$
$\Rightarrow \arg \left(\frac{z-3}{z+i}\right)=-\frac{\pi}{6}$
$\Rightarrow \arg \left(\frac{z+i}{z-3}\right)=\frac{\pi}{6}$