If ${\mathrm{z}}_1, {\mathrm{z}}_2$ are conjugate complex numbers and ${\mathrm{z}}_3,{\mathrm{z}}_4$ are also conjugate, then $\mathrm{Arg}\left(\frac{{\mathrm{z}}_3}{{\mathrm{z}}_2}\right)=$

Given ${\mathrm{z}}_1, {\mathrm{z}}_2$ are conjugate complex numbers, and ${\mathrm{z}}_3,{\mathrm{z}}_4$ are conjugate complex numbers

hence, $arg\left(z_1\right)=-arg\left(z_2\right)$ and $\begin{array}{rcl}arg\left(z_3\right)& =& -arg\left(z_4\right)\end{array}$

Therefore, 

   $\begin{array}{rcl}\mathrm{Arg}\left(\frac{{\mathrm{z}}_3}{{\mathrm{z}}_2}\right)& =& arg\left(z_3\right)-arg\left(z_2\right)\\ & =& -arg\left(z_4\right)+arg\left(z_1\right)\\ & =& arg\left(\frac{z_1}{z_4}\right)\end{array}$