Expired: e ^ (i * π) = -1
Tired: e ^ (i * τ) = 1
Inspired: i ^ i is a real number (!!)

Think of "a^b" as "start at 1. Take the process that 'grows' the number slowly until it reaches a, and repeat it b times"

Think of "i times" as "once, but the process is rotated 90 degrees" (assume we're working on the complex plane)

i is as far from the origin as 1 on the complex plane, so "growing from 1 toward i" is really rotation.

To get to -1, you need to rotate a half circle, hence e^(i*pi) = -1. And a full circle (tau) gets you back to 1.