  Using three different representations of the bicomplex numbers $T\cong
Cl_{C}(1,0) \cong Cl_{C}(0,1)$, which is a commutative ring with zero divisors
defined by $T={w_0+w_1 {i_1}+w_2{i_2}+w_3 {j} | w_0,w_1,w_2,w_3 \in{R}}$ where
${i_1^{2}}=-1, {i_2^{2}}=-1, {j^{2}}=1 and {i_1}{i_2}={j}={i_2}{i_1}$, we
construct three classes of bicomplex pseudoanalytic functions. In particular,
we obtain some specific systems of Vekua equations of two complex variables and
we established some connections between one of these systems and the classical
Vekua equations. We consider also the complexification of the real stationary
two-dimensional Schr{\"o}dinger equation. With the aid of any of its particular
solutions, we construct a specific bicomplex Vekua equation possessing the
following special property. The scalar parts of its solutions are solutions of
the original complexified Schr{\"o}dinger equation and the vectorial parts are
solutions of another complexified Schr{\"o}dinger equation.
