>>11184072This. To complete this proof, you need to define the complex exponential in some way. You can define it as a Taylor series, but that gives an immediate ugly proof for the identity, and show that it is defined everywhere, or you can define it in terms of a simpler ODE. e^x can be defined as the unique solution of y'=y with the right boundary conditions over the complex numbers. Then you need to show that your ODEs solution is e^i\theta
It's only circular if you're using results from a book. If you can prove each statement from elementary principles, it's correct
