New Trigonometric form of The Hamilton's Quaternions

Abstract

Is it possible to define, for certain values n the product of vectors of the real vector space of n dimensions, such that this is, with respect to multiplication and the ordinary addition of vectors, a numerical system which contains the system of real numbers? It can be proven that this cannot be done. In the space of four dimensions this construction is possible if we are apart from the commutativity of the multiplication. The resulting system is the one ofQUATERNIONS. In this work I first do a reminder of the fundamental concepts of Hamilton's Hypercomplex and then a deep work with such concepts.