Some geometric transformations and their connections to complex numbers

In the twelve form textbooks ([2], [3]) are presented some groups of geometric transformations: homotheties, translations, rotations etc. In this paper we will present two geometric transformations and we will show their relationship to groups of complex functions of the same type, namely isomorphic structures: the group of the rotations of a polygon with n vertices and Klein's group. At the end, we will show that the type of the group of the rotations of a regular polygon with four vertices (the square) and Klein's group of geometric transformations exhaust all types of groups of order 4.