This might be a pretty elementary question, but I just want to ensure that my doubts are correct. I was checking my social media today and I accidentally saw one "simple" proof of Euler's Identity. Here is the link: Facebook post. It basically uses integration to show that $\pi = 2i\ln(-1)$.
I highly doubt that this is a valid proof because, in my understanding, you can't show that $\ln(-1)$ or $\ln(i)$ exists without Euler's Equation. Therefore, I see this as a pretty bad pseudo proof. Is my doubt correct?
Here is another weird stuff from the author of the pseudo proof. This so-called "definition" is absolute nonsense for me because you need $e$ to define $\ln$.
