elvishatcher
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So, I was thinking about Euler's formula, and I noticed something interesting. Based on the fact that e^\frac{i\pi}{2} = 1, it seems as though \frac{i\pi}{2} = 0. However, this doesn't make any sense. Not only can I not see how this expression could possibly equal 0, but that would imply that i\pi = 0 which would in turn imply that e^{i\pi} = 1 when it, of course, is equal to -1. At the moment, I have only a very basic understanding of complex/imaginary numbers and their properties, but it seems to me that the implication here is that \ln(1) is not uniquely equal to zero. Is there something I'm missing that shows that this is not the case? If I am correct in this conclusion, is this because of some property of imaginary numbers that I don't know about yet?