A)Let $x,y$ be two complex numbers on the unit circle so that: $\frac{\pi }{3} \le \arg (x)-\arg (y) \le \frac{5 \pi }{3}$ Prove that for any $z \in \mathbb{C}$ we have: $|z|+|z-x|+|z-y| \ge |zx-y|$ B)Let $x,y$ be two complex numbers so that: $\frac{\pi }{3} \le \arg (x)-\arg (y) \le \frac{2 \pi }{3}$ Prove that for any $z \in \mathbb{C}$ we have: $|z|+|z-y|+|z-x| \ge | \frac{\sqrt{3}}{2} x +(y-\frac{x}{2})i|$