Complex analysis:

• $e^{i\theta}=\cos(\theta)+i.\sin(\theta)$
where e is Euler's Number: 2.71828...

In the special case $\theta=\pi$ this reduces to Euler's Identity.

The functions cos and sin come originally from trigonometry, and it's just a little bit magical that they turn up in a purely algebraic context.

Interestingly, the formula also means that in some cases you can take logarithms of negative numbers. Specifically:

 $\log(z)=\log(r.e^{i\theta})=\log(r)+i.\theta$

The log is not unique, though, because the same number z is represented by infinitely many values of $\theta.$