3D colored
We could show every aspect of a complex function on one image if—like before—we create a 3D plot, but now we give meaning also to colors. Let us plot the modulus of the function value and code its phase on the surface using colors. (Naturally the resulting object then should be projected onto a plane.)
We have seen these functions many times now, so we might not need any further commentary.
\(f(z) = z^2\)
\(f(z) = \exp\,z\)
\(f(z) = \sin\,z\)
It is left to the Reader to recall the formerly mentioned properties. How are these reflected on the above pictures?