Imaginary base numbers

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Imaginary base numbers are a non-standard positional numeral system which uses an imaginary number as its radix. The most common is quater-imaginary which uses 2i as it base. The quater-imaginary numeral system was first proposed by Donald Knuth in 1955 as a submission for a high school science talent search.

Imaginary base numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Other imaginary bases are possible too but are not as widely discussed and aren't named.

Write a set of procedures (functions, subroutines, however they are referred to in you language) to convert base 10 numbers to imaginary and back. At a minimum, support quater-imaginary (base 2i).

See Wikipedia: Quater-imaginary_base for more details.

Here are some some decimal and complex numbers converted to quater-imaginary.