While Maxwell's equations certainly can be written with quaternions, they were not originally written that way. Maxwell originally just "wrote them out", meani

While Maxwell's equations certainly can be written with quaternions, they were not originally written that way. Maxwell originally just "wrote them out", meaning component-by-component. He had 20 equations! That's why H is sometimes used for magnetic fields: the electric fields were E, F, and G. Nowadays we usually write 4 vector equations, or 2 in the language of differential forms.