Comment by tsoukase

"God made the integers, all else is the work of man", Kronecker, 1886.

Complex numbers are just a fancy way to represent 2-dimensional numbers that are convenient in geometry through the sq(-1)=π/2 rotation.

They are nothing special and they could just be a matrix. Out of my head I think about complex integers. Also there are higher-order complex numbers which are defined by sq(sq(-1)) etc. In Greek complex numbers are called "mongrel". Both names are bad, I would just use 2-dimensional numbers.