Created At: [[2024-11-11]] ## Basics $ e^{i x} = \cos(x) + i\cdot \sin(x), $ where $e$ is the base of the natural logarithm. Notably, when $x = \pi$, we have: $ \begin{aligned} e^{i\pi} &= \cos(\pi) + i\sin(\pi) \\ &= -1 + i \times 0 \\ &= -1, \end{aligned} $ or, as commonly put, $e^{i\pi} + 1= 0$. This is the **Euler's Identity**.