# 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