real number line, complex plane, ...?

OK so like we put all the real numbers on a single line, and we put all the multiples of the imaginary unit on a single line, and we put those two lines perpendicular to each other and filled in the area with infinitely many lines that are sums of a real part and an imaginary part, forming the complex plane to represent all complex numbers, but I'd like to have that extended to a 3-space.  So did anyone extend complex numbers with another number line at right angles to the real and imaginary number lines so that we could make a 3-space of infinitely many planes?  Maybe stick in that bothersome "divided by zero" thing, I don't know.

>>7
I forgot what a field is

According to my sources, a field is:
1.A land area free of woodland, cities, and towns; open country.

2.A wide, open space that is usually used to grow crops or to hold farm animals.

3.The open country near or belonging to a city -- usually used in plural.

These are the only acceptable definitions of field, period.