The Complex Nonary Number System (WIP)

The "complex nonary" number system is a system with nine digits which can represent "any" complex number as a single number (just like the decimal number system can represent any real number).
This page aims to explain how it works, and its possible use cases.

Note about base 2i

A few number systems similar to this one, with equivalent expressive power, already exist. One example of such a system is base 2i.

Balanced Ternary

The complex nonary number system is inspired by balanced ternary.

The balanced ternary number system (here on wikipedia for a more thorough explanation) has three digits, in this document represented as "-", "0", and "+", which correspond to the values of -1, 0 and 1.
It is a positional number system, where every number is represented as a sequence of digits, sometimes separated into two parts by a dot.

It is "ternary" for two reasons:

1. it has three digits
2. in a number, the value associated to every symbol is multiplied by a power of three corresponding to its place in the number

It is "balanced" because every digit has a corresponding "negative" (0/0, -/+), so it's not "unbalanced" towards a given sign.

Because of this balance, a separate symbol to mark the sign of a number isn't needed; for example, 15 is +--0 (27-9-3+0), and -15 is -++0 (-27+9+3+0).

(other facts to be added sometime in the future)

Complex Nonary

The complex nonary number system has 9 digits, and it can represent any* complex number as a single sequence of digits, with no leading sign, possibly with a decimal point.

The nine digits represent all the coefficients of the type n+mi, with n and m any two integers between -1 and 1 (inclusive).