Thousand Words

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
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 $e^{i\beta}$?

Published September 2004.