Direction : Consider the following for the items that follow :  

Let Z ₁  and Z ₂  be any two complex numbers such that $\rm Z_1^2+Z_2^2+Z_1Z_2=0$

If $x, y$ and $z$ are the cube roots of unity, then what is the value of $xy + yz + zx$?

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, then what is $\operatorname{Re} \left(\frac{z_1}{z_2}\right) + 1$ equal to?