Abstract In complex analysis courses, it is common to use physical interpretations as a didactic tool for teaching complex numbers. In the case of operations between complex numbers, the geometric interpretation of addition and subtraction is well known; however, many authors avoid the interpretation of the multiplication of complex numbers. In this paper, using the physical concepts of rotation and scaling, we will explain the multiplication of complex numbers through visualization in the Argand plane. In addition, we use visual representations in order to obtain proofs without words for some identities.