Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];

vydejRpLp[Rs_,Ls_,ω_]:=Module[{rce,zPar,Lp,Rp,res},
zPar=(1/((1/Rp)+(1/(I*ω*Lp))));
rce={Re[zPar]==Rs,Im[zPar]==ω*Ls};
res=FindRoot[rce,{Rp,10},{Lp,.1}];
{{Rp,Lp},{zPar,Rs+I*ω*Ls}}/.res
];
vydejRpLp[20,0.1,314]

eqs=FullSimplify[{Re[(1./((1/Rp)+(1/(I*ω*Lp))))]==Rs,Im[(1/((1/Rp)+(1/(I*ω*Lp))))]==ω*Ls},{ω>0,Rp>0,Lp>0,Rs>0}]//ComplexExpand//Chop;

vydejRpLp2[Rs_,Ls_,ω_]={Rp,Lp}/.Solve[eqs,{Rp,Lp}][[1]];

vydejRpLp2[20,0.1,314]

ClearAll[vydejC]
vydejC[Rp_,Lp_,ω_,cosfi_]:=Module[{par,c,zRLC,fi,rce,res},
par[list_]:=((Total[(list^(-1))])^(-1));
zRLC=par[{Rp,I*ω*Lp,(1/(I*ω*c))}];
fi=ArcCos[cosfi];
rce=Arg[zRLC]==fi;
res=FindRoot[rce,{c,(10^(-6))}];
c/.res
];
vydejC[100,0.1,314,1.0]

vydejRpLp[Rs_,Ls_,ω_]:=Module[{rce,zPar,Lp,Rp,res},
zPar=(1/((1/Rp)+(1/(I*ω*Lp))));
rce={Re[zPar]==Rs,Im[zPar]==ω*Ls};
res=FindRoot[rce,{Rp,10},{Lp,.1}];
{{Rp,Lp},{zPar,Rs+I*ω*Ls}}/.res
];
vydejRpLp[20,0.1,314]