# How to plot the complex function $f(z) = z^2 + 1$ in a three-dimensional plot with colouring?

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)

For complex function in 3D, you can use ComplexPlot3D,
F[z_] = z^2 + 1;

• Thanks a lot! Is it also possible to show the intersection with $Re(z) = 0$ ? $f(z) = z^2 + 1 = 0$ => $z = i$ and $z = -i$. Just as a visualisation why $f(x) = x^2 + 1$ doesn't intersect with y = 0, but it does when you plot the complex numbers as well. May 4, 2019 at 11:55