# Radix Economy of Complex Bases

If we extend the allowed bases for a numerical system to the complex numbers, is e still the most economic base? If not, what would it be?

There's the well-known formula for radix economy:

Where b is the base, and N is a given number.

I don't know if this formula is still valid for complex numbers. Nonetheless, the only local minimum this function seems to have, even extended over the complex numbers, is at b = e + 0i.

• In the situations that radix economy is trying to model, having a non-real base makes no sense at all. – Yuval Filmus Oct 26 '20 at 7:06