I can't figure out where to start on this one.

Let p(z) = an*z^n+...+a1*z+a0 be a polynomial of degree n with complex coefficients and suppose there exists {z1,...,zn} distinct complex numbers each having Imaginary(zj)>0 such that p(zj)=0 for j∈{1,...,n}. Set q(z)=Real(an)·z^n+...+Real(a1)·z+Real(a0). Prove that if q(w) = 0 then w must be real.

(Here, Imaginary(zj) denotes the imaginary part of zj and Real(aj) denotes the real part of aj.)