[enkimute]

These are also called the planar quaternions and are the even subalgebra of 2D PGA. I use and explain these (and their nD generalisations) in my SIBGRAPI 2021 talk on kinematics and dynamics in PGA.

https://youtu.be/pq9YfdPHhIo

There is also a writeup called 'may the forque be with you' available on bivector.net

[ogogmad]

Looks like there's been some progress on this front since I last looked.

Maybe Wikipedia needs to be updated.