  Previouly a possible extension of the complex number, together with its
connected trigonometry was introduced. In this paper we focuss on the simplest
case of ternary complex numbers. Then, some types of holomorphicity adapted to
the ternary complex numbers and the corresponding results upon integration of
differential forms are given. Several physical applications are given, and in
particuler one type of holomorphic function gives rise to a new form of
stationary magnetic field. The movement of a monopole type object in this field
is then studied and shown to be integrable. The monopole scattering in the
ternary field is finally studied.
