If $|z| = 4$ and $\text{arg}(z) = \frac{5\pi}{6}$,then $z =$

If $z$ and $w$ are complex numbers such that $\bar{z} - i \bar{w} = 0$ and $\operatorname{Arg}(zw) = \frac{3 \pi}{4}$,then $\operatorname{Arg} z =$

If ${z_1}, {z_2} \in \mathbb{C}$,then $\text{amp}\left( \frac{z_1}{\bar{z}_2} \right) = $

If $z_1, z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers,then $\arg \left( \frac{z_1}{z_4} \right) + \arg \left( \frac{z_2}{z_3} \right)$ equals

Argument of the complex number $z = \frac{13-5i}{4-9i}$,where $i = \sqrt{-1}$,is

If $-1 + \sqrt{-3} = re^{i\theta}$, then the value of $\theta$ is