$ e^{ix} = \cos{x} + i \sin{x} $ $e$ = base of the natural logarithm $i$ = imaginary unit $x$ is $\mathbb{R}$ [Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_formula) [Notes on Euler's Formula](https://eli.thegreenplace.net/2024/notes-on-the-euler-formula/) I've always conceptualized complex numbers to behave as if a projection of another dimension onto a lower dimension, and so Euler's