You can think of complex number in some sense as two dimensional numbers. If you think about allowing two dimensions than why not three?
What argument do you have to prefer two over three?
On the other hand you do have arguments for keeping it one dimensional.
Beyond the complex numbers are a whole host of fun number systems, the ‘hypercomplex’ numbers, of which the most popular seem to be the quaternions (with four dimensions) and octonions (with eight).
It seemed a good idea to ask about just ordinary, two-dimensional complex numbers, and find out if there was any use for them in this context, before inquiring about anything more complicated. :)
You can think of complex number in some sense as two dimensional numbers. If you think about allowing two dimensions than why not three? What argument do you have to prefer two over three?
On the other hand you do have arguments for keeping it one dimensional.
Beyond the complex numbers are a whole host of fun number systems, the ‘hypercomplex’ numbers, of which the most popular seem to be the quaternions (with four dimensions) and octonions (with eight).
It seemed a good idea to ask about just ordinary, two-dimensional complex numbers, and find out if there was any use for them in this context, before inquiring about anything more complicated. :)