In pure mathematics complex numbers are a great tool to explore dynamical systems. In this video mathematician Holly Krieger gives an example of a dynamical system and how complex numbers come into the picture.

To find out more about complex numbers and their uses, see this collection of articles and videos. In particular you might want to read What is the Mandelbrot set?.

Holly Krieger is a lecturer at the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, and Fellow and Director of Studies at Murray Edwards College.