Z1=1/(1/(1/(1/(R3+I*w1*L3)+1/R2)+I*w1*L2)+1/R1)+I*w1*L1
Z2=1/(1/(1/(1/(R3+I*w2*L3)+1/R2)+I*w2*L2)+1/R1)+I*w2*L1
Z3=1/(1/(1/(1/(R3+I*w3*L3)+1/R2)+I*w3*L2)+1/R1)+I*w3*L1
Simplify[ComplexExpand[ReIm[Z1]]][[1]]
Simplify[ComplexExpand[ReIm[Z1]]][[2]]
Simplify[ComplexExpand[ReIm[Z2]]][[1]]
Simplify[ComplexExpand[ReIm[Z2]]][[2]]
Simplify[ComplexExpand[ReIm[Z3]]][[1]]
Simplify[ComplexExpand[ReIm[Z3]]][[2]]
Solve[
Z1R==Simplify[ComplexExpand[ReIm[Z1]]][[1]]&&
Z1I==Simplify[ComplexExpand[ReIm[Z1]]][[2]]&&
Z2R==Simplify[ComplexExpand[ReIm[Z2]]][[1]]&&
Z2I==Simplify[ComplexExpand[ReIm[Z2]]][[2]]&&
Z3R==Simplify[ComplexExpand[ReIm[Z3]]][[1]]&&
Z3I==Simplify[ComplexExpand[ReIm[Z3]]][[2]],
{L1,L2,L3,R1,R2,R3}]
Z2=1/(1/(1/(1/(R3+I*w2*L3)+1/R2)+I*w2*L2)+1/R1)+I*w2*L1
Z3=1/(1/(1/(1/(R3+I*w3*L3)+1/R2)+I*w3*L2)+1/R1)+I*w3*L1
Simplify[ComplexExpand[ReIm[Z1]]][[1]]
Simplify[ComplexExpand[ReIm[Z1]]][[2]]
Simplify[ComplexExpand[ReIm[Z2]]][[1]]
Simplify[ComplexExpand[ReIm[Z2]]][[2]]
Simplify[ComplexExpand[ReIm[Z3]]][[1]]
Simplify[ComplexExpand[ReIm[Z3]]][[2]]
Solve[
Z1R==Simplify[ComplexExpand[ReIm[Z1]]][[1]]&&
Z1I==Simplify[ComplexExpand[ReIm[Z1]]][[2]]&&
Z2R==Simplify[ComplexExpand[ReIm[Z2]]][[1]]&&
Z2I==Simplify[ComplexExpand[ReIm[Z2]]][[2]]&&
Z3R==Simplify[ComplexExpand[ReIm[Z3]]][[1]]&&
Z3I==Simplify[ComplexExpand[ReIm[Z3]]][[2]],
{L1,L2,L3,R1,R2,R3}]