I was messing around with some algebra until I came across this: $$0=\ln(1)=\ln(e^{i2\pi n})=i2\pi n,n\in \mathbb{Z}$$ The entire thing seems entirely justified, but I don't understand why it's like this. If anyone could point out an error here, that would be nice.
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See https://math.stackexchange.com/q/4185112/42969 and the linked questions. – Martin R Oct 01 '24 at 05:04
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2Thanks! I didn't realize that it was already a posted question. – SovietWizard Oct 01 '24 at 05:08
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6Complex log is not injective – Gwen Oct 01 '24 at 05:10
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You have a periodic function under the logarithm. – Anixx Oct 01 '24 at 12:18