(or a toddler) Why does “i^i” result in a real number “e^-0.5pi”? How did they figure those out in the first place?

Question

(or a toddler) Why does “i^i” result in a real number “e^-0.5pi”? How did they figure those out in the first place?

In: 9

Answer 1

Although this does not have to be very complicated, if one starts from zero, the story would be rather long for a Reddit comment. But there are excellent series of mini-lectures which cover the subject very well. See here: Eddie Woo [“Complex Numbers”](https://www.youtube.com/watch?v=gHUHZXjpwOE&list=PL5KkMZvBpo5CE__2qeqZQa5e8gSkt1Ypy)