A complex thing made simple with GeoGebra

This article was inspired by Chris Sangwin’s recent contribution on GeoGebra and geometrical functions in MSOR Connections, and, of course, motivated by Markus Hohenwarter’s call for GeoGebra contributions for this issue. The author is grateful to both, as well as to the four students who agreed to have their work quoted here. In his article, Sangwin applies a GeoGebra tool to illustrate Monge’s theorem relating the intersections of certain tangents to circles. With this example he identifies a GeoGebra tool with a geometrical function. However, it was Sangwin’s other example of a geometrical function (or GeoGebra tool), namely the extension of multiplication from the domain of real to that of complex numbers, which led me to ask: how can GeoGebra be used to visualise complex multiplication? Sangwin addressed the question of visualising…