Visualization of Complex Functions in 3D

Given X = x1 + i x2 and Y = y1 + i y2,
given a complex function Y = Y(X), this is a 1D manifold in C^2~(X,Y), or a 2D manifold in R^4~(x1,x2,y1,y2), which means a 4D surface.

Elsewhere we show these 4D visualizations.

Here we show 3D functions z = z(X) relating to Y = Y(X).
Four such functions for each Y:
z = Re(Y), z = Im(Y), z = arg(Y), and z = |Y| .

More at my webpage http://www.wugi.be/qbComplex.html .

Graphing tool: Graphing Calculator 4.0
Music: Bach, contrapunctus 19 (14). It is stopped just where Bach introduces his signature-theme: if I'd tried it on purpose it wouldn't have worked out that nice :-o)

Видео Visualization of Complex Functions in 3D канала Guido Wugi