I made it clear I agreed.
I should have added that it only becomes circular if you add the point at infinity. Otherwise it’s more similar to a plane. But yes, it’s not simply x,y numbers when you assume y^2=-1. The geometric interpretation of the complex numbers matters, and you have to do it correctly. Gets very hard to imagine quickly.
A lot of the confusion in this thread seems to come from people believing that the main idea of complex numbers is that they are just pairs of real numbers.
That is wrong -- pairs of real numbers are just pairs of real numbers. Complex numbers are pairs of real numbers with a particular multiplicative structure.