I'm not sure where the difficulty is but if w is a real number and z is a complex number then w * z = w * (x + iy) = wx + iwy which is a complex number (generally speaking).
You have to remember that the multiplication rules for real numbers are not the same as for complex since you have the i^2 = -1 constraint.
With regards to the question, can you show us your working out for getting the mapping (i.e. the matrix)? Remember that you are sending vectors from the domain into vectors in the co-domain by some linear transformation (your matrix that you are trying to show).