If $|{z_1}|\, = \,|{z_2}|$ and $arg\,\,\left( {\frac{{{z_1}}}{{{z_2}}}} \right) = \pi $, then ${z_1} + {z_2}$ is equal to

If $arg\,z < 0$ then $arg\,( - z) - arg\,(z)$ is equal to

If $\alpha $ and $\beta $ are different complex numbers with $|\beta | = 1$, then $\left| {\frac{{\beta - \alpha }}{{1 - \overline \alpha \beta }}} \right|$ is equal to

If $z_1, z_2, z_3$ $\in$  $C$ such that $|z_1| = |z_2| = |z_3| = 2$, then greatest value of expression $|z_1 - z_2|.|z_2 - z_3| + |z_3 - z_1|.|z_1 - z_2| + |z_2 - z_3||z_3 - z_1|$ is

If ${z_1}.{z_2}........{z_n} = z,$ then $arg\,{z_1} + arg\,{z_2} + ....$+$arg\,{z_n}$ and $arg$$z$ differ by a

If $z$ is a complex number such that $\frac{{z - 1}}{{z + 1}}$ is purely imaginary, then