Re: f(x) = (x^2 + 1) --------- strange (curved Surface) Graph

Op 29/07/2024 om 21:28 schreef HenHanna:

 When   this function      y =  f(x)  =  (x^2  +   1)      is first introduced, we learn its Graph to be a  simple  parabola.
 THEN  when we learn  that  x can be a complex number, so that
the Graph  is    2 (orthogonally) linked   Parabolas.
---------- like this:
 https://phantomgraphs.weebly.com/uploads/5/4/5/4/5454288/4_4_orig.jpg
 https://www.geogebra.org/resource/czbugz9h/fofRh3ZjmwwISd2v/material-czbugz9h-thumb@l.png
   This graph   is   showing a smooth ,  curved  surface   -->
                  https://i.sstatic.net/soSJ8.png
 What is this graph showing???
                 it purports to show    f(x)  =  (x^2  +   1)

Here is one way to visualize it on desmos3d
https://www.desmos.com/3d/8tqp4wqzad
We can verify the plots with wolfram alpha (plotting re(f), im(f), abs(f), arg(f) respectively).
https://www.wolframalpha.com/input?i=plot+arg%28%28x%2Biy%29%5E2-1%29%2C+-5%3Cx%3C5%2C+-5%3Cy%3C5%2Cplotrange+%28-5%2C5%29
My function f is used to map the domain of 0 to 1 for parameters to the range -infinity to infinity.
The function g is used to multiply two complex numbers.