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

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

If the amplitude of $(z-1-2i)$ is $\frac{\pi}{3}$,then the locus of $z$ 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 following complex number into polar form: $\frac{1+7i}{(2-i)^2}$

The argument of the complex number $\frac{13 - 5i}{4 - 9i}$ is