math behind complex numbers C||RLC
At first, I would multiply the numerator N(jw) and the denominator D(jw) with jwC2. As a next step you can rewrite the denominator to get the form D(jw)=R(D)+jIm(D). Use also the identity 1/j=-j.

Because it is your goal to have a denominator that is pure real you can multiply N(jw) as well as D(jw) with the conjugate-complex expression [R(D)-jIm(D)]. Now - because the denominator is real - you can identify the real as well as imag. part of the numerator N(jw). As a last step, both parts must be devided by the real denominator.