Show that $\frac{1}{2}(|z|+|w|)|\frac{z}{|z|} + \frac{w}{|w|}| \le |z+w|$ with $z \neq 0$ and $w\neq0$
Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$