4D visualisation of complex functions w=f(z)

[i]Complex 'Circle-Hyperbola' w=1/z[/i]
Complex 'Circle-Hyperbola' w=1/z
This book is about 'true 4D' visualisations of complex functions w=f(z), where z=x+iy and w=u+iv are complex variables. Most math graphers don't engage in '4D' visualisations, considering them 'impossible'. They confine themselves to 3D-extractions showing graphs of, eg, Re(w) or Im(w), at most suggesting the 4th coordinate with surface coloring. Here we show the 'entire' 4D surface which corresponds to coordinates (z,w=f(z)), admittedly in a projected form (4 axes are projected upon 2D space, a paper sheet or a screen; or upon a '3D' image in 2D), but at least we get a view of the surface in its entirety, not of a 3 coordinate extraction of it! You can see more on this at my web pages wugi's QBComplex: https://www.wugi.be/qbComplex.html wugi's DemoComplex: https://www.wugi.be/qbinterac.html (with Geogebra and Desmos fellow examples) and my Youtube playlists wugi's Visualization of Complex Functions: https://www.youtube.com/playlist?list=PL5xDSSE1qfb6FIk0Pl3VCg5p3Ema52hEG wugi's "olther" Complex Function Graphs: https://www.youtube.com/playlist?list=PL5xDSSE1qfb6Uh98_9vS4BEMEGJB2MZjs