Z1 = (1/(I C1 w))+I L1 w+R1;
w1 = (1/(Sqrt[C1 L1]));
kin1 = (R1/L1); 
kext1 = (z0/(2 L1));

Z1c = ((C1 (-L1) (w^2)+I C1 R1 w+1)/(I C1 w));

Z1c2 =-I L1/ w ((w1^2)-(w^2) +I  w kin1 );

FullSimplify[Z1-Z1c2]

w1box = ((w1^2)-(w^2) +I  w kin1 );