Mathwizurd.com is created by David Witten, a mathematics and computer science student at Stanford University. For more information, see the "About" page.
i, the unit imaginary number, is the square root of -1. What is i^i? It turns out it equals a real number. This post will derive the value, explaining with sufficient rigor while keeping intuition.
Raising a real number to a complex power is actually very similar to real exponentiation. In this article, we derive the value of e^(x + iy), verifying other properties of complex exponentiation.