On the left, a phase portrait of a complex function is displayed. On the right, one can see the approximation of the function through it's Taylor polynomials at the blue base point $z_0$.
The complex function, the base point $z_0$, the order of the polynomial and the zoom can be modified.
Note: The applet was made with Cindy.js and it is based upon Taylor series of complex functions. Thanks to Aaron Montag and Jürgen Richter-Gebert for allowing to adapt their amazing applets. The source can be found at GitHub.