## Most recent change of EulersFormula

Edit made on November 29, 2008 by ColinWright at 11:43:02

Deleted text in red / Inserted text in green

WW
Complex analysis:
* EQN:e^{ix}=cos(x)+i.sin(x)
In the special case EQN:x=\pi this reduces to Euler's Identity.
* EQN:e^{i\theta}=\cos(\theta)+i.\sin(\theta)
where /e/ is Euler's Number: 2.71828...

In the special case EQN:\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:

| EQN:\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 EQN:\theta.