On the Complete Analogy of Complex Analysis and Real Analysis in the Field of Vectors V₂

On the basis of the isomorphic algebraic structures of the field of complex numbers ℂ and the 2-dimensional Euclidean field of vectors V₂, in terms of identical geometric products of elements, this paper brings integral identities for scalar and vector fields in V₂, which are vector analogues of the well-known integral identities of complex analysis. Special attention is paid to the vector analogue of Cauchy's calculus of residues in V₂. At the end of the paper, the algebraic structure of the three-dimensional vector field V₃ is presented, as well as the corresponding fundamental integral identities.