Quater-imaginary base
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Quater-imaginary base is a positional numeral system with a base of 2i, making it an imaginary base. It uses the digits 0, 1, 2, and 3, which makes it a kind of quaternary number system. Unlike real bases, quater-imaginary base can replresent every complex number.
Unfortunately, being only imaginary, it cannot be used for any real applications.