Arguably the best equation in mathematics - well from an engineer's point of view anyway

$$e^{i\theta}=cos{\theta} + i sin{\theta} $$

Apparently this all comes from rotating a unit line in the complex plane - you can Google it if you want to know. There is a special case of this where if you make \(\theta\) equal to \(\pi\) and noting that \(sin \pi = 1\) and \(cos \pi = -1\) it is easy to get Euler's identity:

$$ e^{i\pi} +1 = 0 $$

This is a fascinating equation because it brings together 5 of the most fundamental numbers in maths: \(0, 1, i, e\) and \(\pi\)

Anyway, this post looks at the Euler equation(s) and uses them to do stuff.