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

Consider the following statements:
$I$: If $a$ and $b$ are positive real numbers,then $\sqrt{-a} \times \sqrt{-b} = \sqrt{ab}$
$II$: The argument of $\frac{1+i\sqrt{3}}{1-i\sqrt{3}}$ is $120^{\circ}$
Then:

Convert the given complex number in polar form: $\sqrt{3}+i$

The amplitude of the complex number $\frac{(\sqrt{3}+i)(1-\sqrt{3} i)}{(-1+i)(-1-i)}$ is

Let $z$ be a purely imaginary number such that $\text{Im}(z) > 0$. Then $\text{arg}(z)$ is equal to

The argument of $z = -1 - i\sqrt{3}$ is: