If $arg\,(z) = \theta $, then $arg\,(\overline z ) = $

If $z$ is a complex number, then $(\overline {{z^{ - 1}}} )(\overline z ) = $

Conjugate of $1 + i$ is

If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation

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

If ${z_1} = 1 + 2i$ and ${z_2} = 3 + 5i$, and then $\operatorname{Re} \left( {\frac{{{{\bar z}_2}{z_1}}}{{{z_2}}}} \right)$ is equal to