# Homework Help: Rearrange Euler's identity to isolate i

1. Apr 4, 2014

### Gondur

1. The problem statement, all variables and given/known data

Maybe this is not possible because i does not represent anything quantile and is merely abstract? I'm not sure and maybe you guys can help!

2. Relevant equations

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

3. The attempt at a solution

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

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

You cannot take natural log of a negative number so where do I go from here?

$$ln(e^{i \pi})=ln(-1)$$

$$i \pi=ln((-1))$$

$$i=\frac{ln(-1)}{\pi}$$

2. Apr 4, 2014

### micromass

You would have to take the complex logarithm, which is a subtle little thing.

Last edited by a moderator: May 6, 2017
3. Apr 4, 2014

### 1MileCrash

It is true that ln(-1) = ipi. I don't see anything wrong with what you've said.

You cannot take the ln of a negative in the reals. We are explicitly not limited to the reals.