When we write a real number in base k the n’th digit represents the number of k^n. I’m interested in finding a complex number w such that any complex number z can be written in base w.
I found that w=ai where a is whole doesn’t work because the number of i’s of any number represented in this bad will be divisible by a.
Just to be clear: We can only use digits that are smaller then the absolute value of the base. For example, if the base is 1+i , we can only use 0,1 as the digits ( 1<|1+i|=sqrt(2)<2 ).