Mathematical science is actively developed since the invention of a Cartesian coordinate system <X,Y,Z>. Up to now, the Cartesian coordinate system forms the world view of space matter, its structure and processes occurring in it.

Scientific and technical progress continuously adjusts the coordinate system. Investigation of the structure of matter came to the foreground scene and Cartesian coordinates can be regarded as a first attempt in this direction.

Geometrically Cartesian coordinates are represented by three mutually perpendicular lines outgoing from the zero-dimensional point as a point of intersection of these lines. The geometry of such algebra does not correspond to the three-dimensional space. This deficiency was not corrected in the algebra of vector analysis.

As a result, in science there is no unambiguous link between the representation of numbers and its representation in the space, as this has been achieved in the algebra of complex analysis Cauchy. Planar algebra of complex analysis provides integrated cohesion between the coordinates on the plane (x, y).