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 numb

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.