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

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 $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in [0, 2 \pi],$ is a real number,then an argument of $\sin \theta + i \cos \theta$ is

Convert the given complex number in polar form: $-1+i$

The argument of the complex number $\sin \frac{6\pi}{5} + i(1 + \cos \frac{6\pi}{5})$ is

If $z = \frac{(2-i)(1+i)^3}{(1-i)^2}$,then $\operatorname{Arg}(z) = $