I am trying to solve the problem Secret Code on SPOJ, and it's obviously a math problem.

The full problem

For those who are lazy to go and read, it's like this:

a0, a1, a2, ..., an - sequence of N numbers
B - a Complex Number (has both real and imaginary components)
X = a0 + a1*B + a2*(B^2) + a3*(B^3) + ... + an*(B^n)

So if you are given B and X, you should find a0, a1, ..an. I don't know how or where to start, because not even N is known, just X and B.

The problem is not as easy as expressing a number in a base B, because B is a complex number.

How can it be solved?