If $z$ is a complex number of unit modulus and argument $\theta$,then $\text{arg}\left( \frac{1+z}{1+\bar{z}} \right)$ equals:

The amplitude of $\sin \frac{\pi}{5} + i(1 - \cos \frac{\pi}{5})$ is

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

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:

If $z_1 = 5 - 2i$ and $z_2 = 3 + i$,where $i = \sqrt{-1}$,then $\arg \left(\frac{z_1 + z_2}{z_1 - z_2}\right)$ is

Match the items of List-$I$ with those of List-$II$:

List-$I$ (Complex number)	List-$II$ (Polar form)
$(i) \sqrt{3}-i$	$(a) 2 \operatorname{cis} \frac{\pi}{6}$
$(ii) \sqrt{3}+i$	$(b) 2 \operatorname{cis} \frac{5 \pi}{6}$
$(iii) -\sqrt{3}+i$	$(c) 2 \operatorname{cis}\left(-\frac{5 \pi}{6}\right)$
$(iv) -\sqrt{3}-i$	$(d) 2 \operatorname{cis}\left(-\frac{\pi}{6}\right)$

The correct matching is: