[math-fun] Radix-r numbers; |r|=1, r=log(ik)

Approximately represent complex numbers in radix r, where r=log(ik), for some integer k>0, i=sqrt(-1). Several choices of numerals: {0,1}, {0,i}, {0,1,i}, {0,+-1,+-i}. So |r|=1, and we have good approximations to *random walks*. This is not a particularly efficient number system, so is there an efficient algorithm to compute an approximation?