Re:Why does e to pi i equal -1? (2015) [video]
by cousin_it on Tuesday February 14, 2017 @03:01PM
(#13646613)
Sure, step 1 relies on the existence of e^z which is not obvious. Step 2 relies on the chain rule over C, step 4 relies on having a unique solution to a differential equation, etc. My comment can be expanded to a proof, but it was more aimed to explain why Euler's identity is natural.
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Re:Why does e to pi i equal -1? (2015) [video]
by ouid on Tuesday February 14, 2017 @07:04PM
(#13648536)
step 1 isn't "not obvious"; it's nonsense. What, exactly, are you trying to prove exists? e^z? e^z is undefined at this point. If you're trying to prove that e^i\pi=-1, you need to start with a definition of e^z.