So many people in the replies here are totally missing the point. Yes, there is an infinite number of valid possible answers for i^i. But EVERY SINGLE ONE OF THEM IS A REAL NUMBER.

So many people in the replies here are totally missing the point. Yes, there is an infinite number of valid possible answers for i^i. But EVERY SINGLE ONE OF THEM IS A REAL NUMBER.

https://x.com/mathladyhazel/status/1800905395961241811

i^x = rotation (counterclockwise)
^i = "take the operation you were doing, and rotate *that operation itself* by another 90 degrees counterclockwise

Hence i^i = move along the vector going counterclockwise along the circle, rotated another 90 degrees = move along the vector going direct toward the origin

I think about it like this:

i is a number in 2D, and some operations on it end up in one axis (the real axis in this case). If you visualize it, it is easier. Although you started with a number or a vector on 2D, this specific operation lands on 1D always

People on Twitter are missing the point? I'm shocked!

I thought replies were (italics) for missing the point?

i^i 

Looks like an emoji for the dog from adventure time

Can any giga brain explain me what the math is? 🥲

It's like the universe, infinite but there is an exact number of galaxies. But counting them takes forever.

Vetalik on the way to creating contracts for the universe

i^i =(e ^ iπ/2)^i = e ^ -π/2 ≈ 0.20788