I have two real polynomials that depend in variables (xi1, xi2) and parameters (eps, e2). I apply the following complexification:

(xi1, xi2, eps, e2) = gamma1(xi1, xi2, eps, e2) + I gamma2(xi1, xi2, eps, e2)

Now I wish to define the variable z = xi1 + I xi2, and find a neat expression w in z and it's conjugate, zc, as follows:

w(z, zc) = c30 z^3 + c21 z^2 zc+ c12 z zc^2 + c03 zc^3 + o(3)

In order to find the coefficients.

How may I ask this to Mathematica?