If $z=x+iy$ and $z^{1/3}=p+iq$,where $x, y, p, q \in R$ and $i=\sqrt{-1}$,then the value of $\left(\frac{x}{p}+\frac{y}{q}\right)$ is

The value of $(1+i)^5(1-i)^7$ is:

If $x+iy = \frac{3}{2+\cos \theta + i \sin \theta}$,then $x^2+y^2 =$

If $\left|z-\frac{2}{z}\right|=2$,then the greatest value of $|z|$ is

Consider the following two statements:
Statement $I$: For any two non-zero complex numbers $z_1, z_2$,
$(\left|z_1\right|+\left|z_2\right|)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2(\left|z_1\right|+\left|z_2\right|)$
Statement $II$: If $x, y, z$ are three distinct complex numbers and $a, b, c$ are three positive real numbers such that $\frac{a}{|y-z|}=\frac{b}{|z-x|}=\frac{c}{|x-y|}$,then
$\frac{a^2}{y-z}+\frac{b^2}{z-x}+\frac{c^2}{x-y}=1$
Between the above two statements,

If $z=\cos 6^{\circ}+i \sin 6^{\circ}$,then $\sum_{n=1}^{20} \operatorname{Im}\left(z^{2 n-1}\right)=$