No, they're just plane geometry, albeit in a cludgy notation (which conflate vectors and rotation operators on vectors because they happen to be isomorphic in R^2). But plane geometry is a real thing.
Imaginary numbers are just 2D vectors. Its such a horrible name. The imaginary part isnt any more mysterious than the real part. Theyre just orthogonal properties.
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.
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.
