If$z = \frac{{1 - i\sqrt 3 }}{{1 + i\sqrt 3 }},$then $arg(z) = $ ............. $^\circ$

Let $z _{1}$ and $z _{2}$ be two complex numbers such that $\overline{ z }_{1}=i \overline{ z }_{2}$ and $\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi$. Then

If $Arg(z)$ denotes principal argument of a complex number $z$, then the value of expression $Arg\left( { - i{e^{i\frac{\pi }{9}}}.{z^2}} \right) + 2Arg\left( {2i{e^{-i\frac{\pi }{{18}}}}.\overline z } \right)$ is

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

If ${z_1},{z_2}$ are two complex numbers such that $\left| {\frac{{{z_1} - {z_2}}}{{{z_1} + {z_2}}}} \right| = 1$ and $i{z_1} = k{z_2}$, where $k \in R$, then the angle between ${z_1} - {z_2}$ and ${z_1} + {z_2}$ is

If the equation, $x^{2}+b x+45=0(b \in R)$ has conjugate complex roots and they satisfy $|z+1|=2 \sqrt{10},$ then