That is correct. In the Clifford formulation that is equivalent (and in general a superset) of complex numbers you can choose the dimension or behavior to be wh

That is correct. In the Clifford formulation that is equivalent (and in general a superset) of complex numbers you can choose the dimension or behavior to be whatever you want it to be in the resulting algebra. You can even assign it a particular metric or nullify it. The 'square to -1' that implies quadrature is just a specialization in that case. Many algebraic things of complex numbers like the exponential map still work or have general counterparts.