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

The whole point of the question is for you to find the right
diagrams. You need to know that the distance between two points $a$
and $b$ in the complex plane (Argand Diagram) is given by
$|a-b|$.

By definition $e^{i\alpha}= \cos \alpha + i\sin \alpha$ so
where does this lie in the complex plane? Now what about
$e^{i\beta}$?