I've noticed that there are different ways to plot a complex function. What I am interested in, is a three-dimensional plot with colouring of the complex function $f(z) = z^2 + 1$. Here is an example of a plot of another random complex function:
Is it possible to plot this specific complex function in the same manner? I've tried using Wolfram|Alpha, but it only gives me a two-dimensional plot with only real numbers. I've also used other sites, which gives me a two-dimensional plot with domain colouring. Could someone perhaps use the same type of plot as in the example above to plot the specified complex function $f(z) = z^2 + 1$?
(Not two separate plots of the real part and the imaginary part, or the input and output)