# Complex Plane Dimension Number

What dimension between space-time and 11 Dimensions is allocated to the complex plane 'visualized' and used in complex number theory?

Complex numbers are used in every branch of maths and physics, based on an imaginary complex plane, z = x +iy where y is an imaginary axis and i^2=-1. - It's another Dimension, the imaginary '5th' dimension.

In the current theories, what is name or number of is this dimension apart from the obvious 'imaginary dimension' - what number is it given?

Regards

Terry Giblin

You seem to be mixing up several concepts in physics and mathematics
that are different.

To properly visualize a complex function like $$f(z) = z^\frac{2}{3}$$,
you would like 4 dimensions because the domain of the function is two-dimensions
and so is the range. This can't be done easily, so people usually plot |f(z)| which
is a scalar against z which is two dimensional. The result is a three-dimensional
surface plot.

mathman
What dimension between space-time and 11 Dimensions is allocated to the complex plane 'visualized' and used in complex number theory?
You are mixing up two different (although similar in some ways) concepts. The 11 dimensions of brane theory are physical dimensions, like space and time. The complex plane is a mathematical abstraction. One obvious difference is that for physical dimensions the numbers are in units of length or time, which can be changed (like from feet to meters). The numbers in the complex plane are absolute, e.g. 1 is 1 and nothing else - there is no concept of feet or seconds.