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Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence.

We show a transformation K which allows us to rewrite the Dirac equation in its covariant form in a purely real quaternionic equation. We discuss how this transformation allows us for obtaining a involutive symmetry of the Dirac equation, as well as one simplification of the traditional vector of currents of the Dirac equation in traditional form. We also show the corresponding quaternionic equation for the problem of charge conjugation in the hole theory, and the quaternionic equation of conservation of currents. Finally, we discuss one decomposition of the quaternionic Dirac operator in two Maxwell's operators corresponding to time-harmonic case in homogeneous media, without sources which surprisingly agrees with the well known relation in quantum mechanics between the frequency ù and the impulse p E=p²c²+m²c, where E denotes the energy.