The argument of the complex number $ - 1 + i\sqrt 3 $ is ............. $^\circ$

Let $\bar{z}$ denote the complex conjugate of a complex number $z$ and let $i=\sqrt{-1}$. In the set of complex numbers, the number of distinct roots of the equation

$\bar{z}-z^2=i\left(\bar{z}+z^2\right)$ is. . . . . .

$arg\,(5 - \sqrt 3 i) = $

Let $S=\left\{Z \in C: \bar{z}=i\left(z^2+\operatorname{Re}(\bar{z})\right)\right\}$. Then $\sum_{z \in S}|z|^2$ is equal to

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

Given $z$ is a complex number such that  $|z| < 2,$ then the maximum value of $|iz + 6 -8i|$ is equal to-