I've worked with Euler's Identity for physics applications quite a few times, but ran into a "proof" of a contradiction in it, which I can't seem to find a flaw in (the only time I've ever had to do any proofs was in high school). I've derived Euler's equation in two different ways in past classes, so I know it works, but I'm at a bit of a loss here.(adsbygoogle = window.adsbygoogle || []).push({});

## e^{i\theta} = cos{\theta} + isin{\theta} ##

Set ##\theta = 2\pi ##

## e^{2\pi i} = cos{2\pi} + isin{2\pi} ##

## e^{2\pi i} = 1 ##

Take the natural log:

## ln{e^{2\pi i}} = ln{1} ##

## 2\pi i = 0 ##

## i = sqrt{-1} = 0 ##

## -1 = 0 ##

I think the problem was in using the natural log up there, but I'm not positive.

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# Problem in apparent contradiction in Euler's Identity?

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