(a)We have ${z_2} = {\overline z _1}$and ${z_4} = {\overline z _3}$
Therefore ${z_1}{z_2} = |{z_1}{|^2}$and ${z_3}{z_4} = |{z_3}{|^2}$
Now $arg\left( {\frac{{{z_1}}}{{{z_4}}}} \right) + arg\left( {\frac{{{z_2}}}{{{z_3}}}} \right) = arg\left( {\frac{{{z_1}{z_2}}}{{{z_4}{z_3}}}} \right)$
$ = arg\left( {\frac{{|{z_1}{|^2}}}{{|{z_3}{|^2}}}} \right) = arg\left( {{{\left| {\frac{{{z_1}}}{{{z_3}}}} \right|}^2}} \right)= 0$
(Argument of positive real number is zero).