Thousand Words

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 $\alpha> \beta$

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

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Published September 2004.