3 ms·
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 differe
by cousin_it 10y ago
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.
- ouid 10y agostep 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.