Quaternions for electromagnetic equations:
Maxwell's original formulas for electromagnetism were done using quaternion math and only later Oliver Heaviside created an overly condensed, pasterized and simplifed version in the form of the 4 partial differential equations people use today.
There is a fundamental problem with Heavyside's version in that they can no longer readily represent matter and energy's motion through time in any direction other than what we imagine is the forward direction (or its opposite) that we imagine all energy to flow in. There is the possibility that motion through time is better represented in 3 directions related to the 3 dimensions of space.



Please see more details about how energy flows through time:
https://www.vasantcorporation.com/natureoftime.php
Mathematicians have historically presumed that when they end up with negative or imaginary directions in time that their equations must not represent real world possibilities and then they abondon or alter their equations for different math. This is a mistake.
In order to represent energy moving in other "phases" in spacetime or transitioning from our phase in spacetime to some other phase, it may be more easily done with quanternions. There have been many witnesses of UFOs that are either partially transparent or that dissappear completely. They are seeing the effects of moving matter from one phase in spacetime to another.
These other phases are not totally devoid of matter except for the UFO that transitions to and from these other phases. There are other things there already just as there are lots of things here in our phase of spacetime.
Please carefully study the above paper about the nature of time lest the above statements about "phases" in spacetime will sould like gibberish.
Maxwell's Equations:
Quaternion links:
Electromagnetics:
Electromagnetics, the Original Quaternions 