# Eulers Identity

1. May 7, 2010

### xvtsx

1. The problem statement, all variables and given/known data
Okay, yesterday in class my teacher gave me this identity $$e^{i\pi }+1=0$$
and she wants me to rearrange the numbers around, so I can get this $$i^{i}= e^{-\frac{\pi}{2}}$$

2. Relevant equations and 3. The attempt at a solution
I know that if Isolate the 1 to the other side and take the square root of each sides I will have this $$\sqrt{e^{i\pi }}= \sqrt{-1}$$
But this is the question what do I do after that ?

Last edited: May 7, 2010
2. May 7, 2010

### jbunniii

Do you know another way to write

$$\sqrt{e^{i \pi}}$$?

Do you know another way to write

$$\sqrt{-1}$$?

3. May 7, 2010

### tiny-tim

Hi xvtsx!

(have a pi: π and try using the X2 tag just above the Reply box )

Raise each side of your last equation to the power of i.

4. May 7, 2010

### xvtsx

Hmm.. do I raise to the power of i after I change the square root for $$\frac{1}{2}$$ and multiple it with $$iπ$$ ?

Last edited: May 7, 2010
5. May 7, 2010

### tiny-tim

(what happened to that π i gave you? )

Yes, (eiπ/2)i = … ?

6. May 7, 2010

### xvtsx

sorry for the pi part, but I use the latex editor and it only gaves that one xD.. thanks by the way. :)