If $Arg(z)$ denotes the principal argument of a complex number $z$,then the value of the expression $Arg\left( -i e^{i\frac{\pi}{9}} z^2 \right) + 2Arg\left( 2i e^{-i\frac{\pi}{18}} \bar{z} \right)$ 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:

Convert the complex number $\frac{-16}{1+i \sqrt{3}}$ into polar form.

$arg(5 - \sqrt{3}i) = $

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 $z_1 \cdot z_2 \cdot \dots \cdot z_n = z$,then $arg(z_1) + arg(z_2) + \dots + arg(z_n)$ and $arg(z)$ differ by a