This simulation illustrates why the famous Euler's Identity
holds, by utilizing the following equation: $$e^x = \lim_{n\to\infty} (1 + \frac{x}{n})^n$$, which holds for any complex number $x$.
Check out the results for different values of $n$, or simply click on "Animate to n = 128".
As you will see, as $n$ gets larger and larger, $(1 + \frac{i\pi}{n})^n$ gets closer and closer to -1.