I think you only need to double the number of digits for base 2i compared to base 2, rather than square it. Also for the curious, there is a Wikipedia article about this (though math Wikipedia is usually pretty obtuse): https://en.wikipedia.org/wiki/Quater-imaginary_base
Takes me back to my early programming classes, going over binary and hexadecimal.
‒ I enjoyed this!
‒ I encourage you to use “\times” in LaTeX rather than “*” to represent multiplication (of numbers).
‒ This is the first essay I can remember reading that would have been better as a video. (Obviously I don’t begrudge you for doing it this way.)
I think you only need to double the number of digits for base 2i compared to base 2, rather than square it. Also for the curious, there is a Wikipedia article about this (though math Wikipedia is usually pretty obtuse): https://en.wikipedia.org/wiki/Quater-imaginary_base
I am happy to learn this thing exists outside the confines of my beloved grandparents' long-departed printer paper!