Z1 = R1;
Z2 = ((-I)/(C w));
Solve[(1/Z1) + (1/Z2) == (1/Z), Z]

ComplexExpand[-((I R1)/(-I + 
              C R1 w))]

Z2 = I L w;
Solve[(1/Z1) + (1/Z2) == (1/Z), Z]

ComplexExpand[((L R1 w)/(-I R1 + L w))]