Only marginally related, but I spent one of my summers at PROMYS[1] doing research into which complex numbers could be successfully used as bases. As different as the various common integer bases "feel" in terms of hand-computation, there's nothing like cranking out conversions of fractions to base 1+i to make you realize that there's a whole wacky universe of number representations out there. I thought it was a really cool field of study, and I remember wishing there were more readily apparent applications. Anyone?
Donald Knuth developed the "quarter-imaginary number system" (based on 2i) for a high school talent search. It can represent every complex number with just the digits 0,1,2 and 3, without the use of a sign character.
[1] https://www.promys.org/