Quaternionic comparisons of electromagnetism using Lorentz transformations

In this paper, by defining properties of the real and complex quaternion algebras, the electromagnetic field equations including monopoles have been studied in $$\hbox {S}'$$ reference systems, which moves with the velocity u according to the fixed reference system $$\hbox {S}$$. Quaternionic source and wave equalities have been derived in a more compact and elegant manner in $$\hbox {S}'$$ system. Besides, Poynting theorem has been firstly obtained in moving media. Additionally, the comparisons between $$\hbox {S}$$ and $$\hbox {S}'$$ reference systems have been separately done for field, source, potential and wave equations in quaternion basis elements. Furthermore, Poynting theorems have been compared by means of $$\hbox {S}$$ and $$\hbox {S}'$$ systems for the first time.