> except for the rules how to calculate with them But this is crucially important. The complex numbers is an (algebraically closed) field. Vectors comprise, we

> except for the rules how to calculate with them But this is crucially important. The complex numbers is an (algebraically closed) field. Vectors comprise, well, a vector (linear) space. Most useful vector spaces have the dimension greater than 2. (In fact, when the complex numbers are thought of - rarely - as vectors space, it is a 1-dimensional complex vector space.)