Thousand Words
Age 16 to 18
Challenge Level
Draw a simple diagram which makes it clear that the following
inequality holds for any complex numbers $z$ and $w$ $$|z-w|\geq
|z| -|w|$$
Now draw another simple diagram which makes it clear that the
following inequality holds for any real numbers $\alpha>
\beta$
$$|e^{i\alpha}-e^{i\beta}|\leq \alpha - \beta$$