Geometrie and Analytic Problems on Bicomplex Plane.

Let us recall that the bicomplex plane is a complex ring of complex dimension 2. It consists of couples of the kind (z, w) = z + jw, where z and w are complex numbers and j is a symbol with the property j² = -1. We note that the bicomplex plane admits singular points. The set of these singular points coincides with the cross-choped set of complex bisectrices (z, ±z), z is a complex. The main problem in the function theory on the bicomplex plane is to describe the interconnection between the same theory of the cross-choped subset and whole bicomplex plane. The first theory is of one complex variable and the second one is of two complex variables. Another problems are related with the comformal mappings and the movement of a partíais of this subset on the whole one. Presented paper is a start studies in this direction. [ABSTRACT FROM AUTHOR]