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

Standing on the shoulders of giants 🌌
idanlevin.xyz

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

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

The idea that every solution for i^i is a real number challenges our intuition and showcases the beauty and complexity of mathematics. Sometimes, diving deeper into the details reveals unexpected truths. 📐✨

i^i is not only a real number, but also equal to e^(-π/2), if you use Euler’s formula.

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

including 11,025!!!
What a weird sentiment.

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

i^i 

Looks like an emoji for the dog from adventure time

I thought that's how math works, sometimes you just abstract numbers