Let $z$ and $w$ be two distinct non-zero complex numbers. If $|z|^2 w - |w|^2 z = z - w$,then:

The value of $4x^3 - 4x^2 - 7x + 127$ when $x = \frac{4 + 5i}{2}$ is

If $z(1 + a) = b + ic$ and $a^2 + b^2 + c^2 = 1$,then $\frac{1 + iz}{1 - iz} = $

The biquadratic equation,two of whose roots are $1+i$ and $1-\sqrt{2}$,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,

Which of the following are correct for any two complex numbers $z_1$ and $z_2$?