\\ $arg$ \left (\frac{1+z}{1+\bar{z}} \right ) = $ arg$(1+z) $ $- $ arg$(\overline{1+z}) = 2$ arg$(1+z) \\\\ $From sketch, $ 2$ arg$(z+1)= $ arg$(z) $ (isosceles triangle, exterior angle of triangle equals sum of opposite interior angles)$ \\\\ $Thus, $ $arg$\left(\frac{1+z}{1+\bar{z}}\right) =...