1. Sep 29, 2004

### DennisG

ok, so I saw this thing one time that looked like this:

e^(pi*i) = - 1

can anyone tell me what this is, what it's used for, and especially how it works? A friend showed me the equation one time, but neither of us knew a thing about it.

Dennis

2. Sep 29, 2004

### newPatrick

Its Euler formula coming from the expansions of sinx, cosx, e^x
e(PI^i)=cis(PI)=-1

3. Sep 29, 2004

### Integral

Staff Emeritus
So as not to be to repetitive, see this thread

Last edited: Sep 29, 2004
4. Sep 29, 2004

### Zurtex

I'm going to assume from the way you asked the question that you don't know what e is in the 1st place? (Please don't take this as an offence if you do know it)

There are lots of definitions of e, it is probably the most important number in calculus. Here are a few definitions:

$$e = \sum_{n=0}^{\infty} \frac{1}{n!} = \lim_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right)^x$$

Also:

$$\frac{d}{dx} \left( e^x \right) = e^x$$

And:

$$\int_1^e \frac{dx}{x} = 1$$

Edit: Amended thanks to below post.

As well as:

$$e = 2.718281828459045235326 \ldots$$

As for the result:

$$e^{\pi i} = -1$$

This comes from some maths orientated around complex numbers which yields the formulae:

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

Hope that helps.

Last edited: Sep 29, 2004
5. Sep 29, 2004

### Integral

Staff Emeritus
I posted the link to the other thread in hopes that further posts on this topic would be in the existing thread.

EDIT: Oh yeah, I forgot to mention

$$\int^e _1 \frac {dx} x = 1$$ not e.

Last edited: Sep 29, 2004