GeoGebra, Complex Maps and Riemann Sphere

Abstract

This paper gives a vision of the work we have been carried out over the past two years, presented at the meetings “III Dia GeoGebra Portugal”, Aveiro University, May, 2013” and “IV Dia GeoGebra Portugal”, Superior School of Education of Oporto Polytechnic Institute, May 2014, and the improvements done so far having in mind didactical purposes. In the first meeting, we have shown how we could use GeoGebra to create colouring domains enabling the representation of complex function graphics and opening a promising path for the exploration of properties of functions of two real variables. In the second meeting we have unveiled the relation between Mobius transformations and the movements of a Riemann Sphere. Now our focus of attention is in the use of this software as a tool for learn, teach and research complex analysis.