If $-1 + \sqrt{-3} = re^{i\theta}$,then $\theta$ is equal to

If $Z_1$ and $Z_2$ are complex numbers such that $|Z_1+Z_2|=|Z_1|+|Z_2|$,then the difference in the amplitudes of $Z_1$ and $Z_2$ is

If for complex numbers $z_1$ and $z_2$,$\arg(z_1/z_2) = 0$,then $|z_1 - z_2|$ is equal to

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$ then $\text{arg}({z_1}) - \text{arg}({z_2})$ is equal to

Let $z$ satisfy $|z|=1$, $z=1-\bar{z}$ and $\operatorname{Im}(z) > 0$.
Statement-$I$: $z$ is a real number.
Statement-$II$: Principal argument of $z$ is $\frac{\pi}{3}$.
Then

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: