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^

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.