Consider the following two statements: Statement I: For any two non-zero complex numbers z_1, z_2 (|z_1|+|z_2|)|z_1/(|z_1|)+z_2/(|z_2|)| ≤…

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