We construct solutions of a time-harmonic Maxwell-type system within the framework of the algebra of complex quaternions. Using quaternionic analysis, we establish a connection between this system and certain first-order differential operators whose kernels consist of monogenic functions. Building on known representations of harmonic and monogenic functions, we develop a constructive procedure based on transmutation operators for generating explicit solutions of the equations (D±λ)u=0, and consequently of the corresponding Maxwell system. This approach provides a systematic method for reconstructing electromagnetic fields from harmonic and monogenic data, yielding an explicit link between quaternionic operator theory, transmutation methods, and the classical formulation of Maxwell equations.
Pablo E. Moreira (Tue,) studied this question.