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## 'Thousand Words' printed from http://nrich.maths.org/

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 $\alpha>
\beta$

$$|e^{i\alpha}-e^{i\beta}|\leq \alpha - \beta$$