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.

A complex number is actually a 2D vector. It has two values. So what is the third value you're adding to make it a 3D vector?

>>2
yeah I was wondering if anyone came up with a third thing, to satisfy my desire for a kind of number that would be represented in three axes, having complex numbers as a single plane subset of them

Try a Hilbert space.

What do you expect from your three dimensional extension of the complex numbers?
Do you want it to be a field? A skew field? Is maybe a vector space enough for you?

>>5
pika pika pikarin~ jan ken pon~

>>5
whatever feels good, man.  I forgot what a field is and I'm too lazy to look it up.

>>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.

>>8
oh well those sound pleasant

>>8
What about form fields? :<

fuck infinityD vectors, I want my knuth arrows generalized into non-integer amount of arrows
trying to run an evolutionary program even as we speak, but it won't converge
i think they haven't even defined tetration well enough yet, but the graphs on the wikipedia page look awesome and psychedelic:
http://upload.wikimedia.org/wikipedia/commons/3/32/Tetration_escape.png
http://upload.wikimedia.org/wikipedia/commons/0/05/Tetration_analytic_extension.svg
they somewhat resemble the exponential map though,
i can't wait to see what the generalized superfunction of addition looks like, this stuff makes me think inherent nature of existence itself, happy, cruel and serene like God :3