Use a diagram to prove that the following inequality holds for all complex numbers $z$ and $w$

${\displaystyle \Vert z-w\Vert \geqq \Vert z\Vert -\Vert w\Vert .}$

Now use another diagram to prove the following inequality

${\displaystyle \Vert e^{i\alpha }-e^{i\beta }\Vert \leqq \alpha -\beta }$

where $\alpha \geqq \beta$.