If $arg(z) < 0$,then $arg(-z) - arg(z)$ equals

Assertion $(A)$: If the arguments of $\bar{z}_1$ and $z_2$ are $\frac{\pi}{5}$ and $\frac{\pi}{3}$ respectively,then $\arg(z_1 z_2)$ is $\frac{2\pi}{15}$. Reason $(R)$: For any complex number $z$,$\arg(\bar{z}) = \frac{\pi}{2} + \arg(z)$. The correct option among the following is:

If the amplitude of $(z-1-2i)$ is $\frac{\pi}{3}$,then the locus of $z$ is

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

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:

Convert the following into polar form: $\frac{1+3i}{1-2i}$