> Imaginary numbers are just 2D vectors.

You meant complex numbers. I wrote "imaginary numbers" on purpose.

> The imaginary part isnt any more mysterious than the real part.

What's surprising is that imaginary numbers are required for QM. Not the 2d vector in one variable trick, actual imaginary numbers.

See for example: https://www.nature.com/articles/s41586-021-04160-4

I think that paper is saying that you have to use N independent 2D numbers, not 2N independent 1D numbers.

Complex numbers are literally the same as 2D real numbers with the rotational symmetry constraint.

https://www.reddit.com/r/Physics/comments/11ujjjd/quantum_th...

What are imaginary numbers if you remove its relation to the real numbers? Do they not become regular real numbers?

How I am seeing it, real and imaginary numbers are both equivalent constructions with the same properties/construction (you can add/substract/multiply/divide them the same way), and its only in the context of using both (in the context of the complex numbers), that they can be differentiated.

They’re not “just” 2D vectors, they have a bit more structure that makes them special, but sure there’s obviously nothing “imaginary” about them.

They are imaginary in the same way that Banach Tarski theorem is a paradox.

That's not quite right. Imaginary numbers are vectors with angle addition via multiplication. Real numbers all have zero angle, so their angle addition is trivial.

Is that a property of imaginary numbers, or a property of relating two orthogonal numbers? Legitimately asking because I can't find any special properties that imaginary numbers alone have in relation to themselves.