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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Algebraic Manipulation of Euler's Identity Leads to a Strange Result

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