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

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)