Rearrange Euler's identity to isolate i

[Gondur]

Homework Statement

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!

Homework Equations

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

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?

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

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

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

 

[micromass]

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

https://www.physicsforums.com/showthread.php?t=637214

 

[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.