How to write a complex number in terms of a complex base.

Question

When dealing with real numbers, we can easily write a integer $ X $ easily in terms of base $ Y $. $$ X= \sum_{k=0}^n a_k Y^k $$ where $0 <=a_k <Y $, The conversion is easy by a simple algorithm but how can we do the same for complex numbers?

Answer 1

You do it just the same for the real and imaginary parts separately. When you write $z=a+bi$ you can express $a$ and $b$ however you want.