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.