- #1
amolv06
- 46
- 0
I was playing around with Euler's identity the other day. I came across something that seems contradictory to everything else I know, but I can't really explain it.
I started with
[tex]e^{i\pi} = -1[/tex].
I rewrote this as
[tex]ln[-1] = i\pi[/tex]
Multiplying by a constant, we have
[tex]kln[-1] = ki\pi[/tex]
and using log properties I arrived at
[tex]ln[-1^{k}] = ki\pi[/tex]
Now if I set k equal to any even number, I have
[tex]ln[1] = 0 = ki\pi[/tex]
This seems to imply that [tex]i\pi[/tex] is 0, however it is not. Furthermore, any even value of k gives the same answer. Why is this?
I started with
[tex]e^{i\pi} = -1[/tex].
I rewrote this as
[tex]ln[-1] = i\pi[/tex]
Multiplying by a constant, we have
[tex]kln[-1] = ki\pi[/tex]
and using log properties I arrived at
[tex]ln[-1^{k}] = ki\pi[/tex]
Now if I set k equal to any even number, I have
[tex]ln[1] = 0 = ki\pi[/tex]
This seems to imply that [tex]i\pi[/tex] is 0, however it is not. Furthermore, any even value of k gives the same answer. Why is this?