The argument of the complex number $\frac{13 - 5i}{4 - 9i}$ is

Let $z$ and $w$ be two complex numbers such that $\bar{z}+i \bar{w}=0$ and $\operatorname{Arg}(z w)=\pi$. Then,$\operatorname{Arg} z=$

If the $\operatorname{Arg} z_1$ and $\operatorname{Arg} \overline{z_2}$ are $\frac{\pi}{3}$ and $\frac{\pi}{5}$ respectively,then the value of $\operatorname{Arg} z_1 + \operatorname{Arg} z_2$ is

The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} + i}$ is

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 $z_1 = -\sqrt{3} + i$ and $z_2 = -\sqrt{3} - i$,then the principal amplitude of the complex number $\frac{z_1}{z_2}$ is