ω=314.;
T=((2Pi)/ω);
Uz=230*(Sqrt[2])*Sin[ω*t+0.4];
R=15;
L=0.2;
eqns={u1[t]==Uz,u1[t]-u2[t]==R*i[t],u2[t]==L*i'[t],i[0]==0};
tmax=5T;
sol=NDSolve[eqns,{u1,u2,i},{t,0,tmax},StartingStepSize->(10^(-11))][[1]];
pl1=Plot[i[t]/.sol,{t,0,tmax},AxesLabel->{"t [s]","i [A]"},PlotStyle->Thick]

sin1=10Sin[ω*t+0.6];
sin2=15Sin[ω*t+1.8];
phasor1=10*(E^(I*0.6));
phasor2=15*(E^(I*1.8));
sumphasor=phasor1+phasor2;
sumsignal=Im[sumphasor*(E^(I*ω*t))]

Plot[{sin1+sin2-sumsignal},{t,0,tmax},AxesLabel->{"t [s]","i [A]"},PlotStyle->Thick]

Uz = 230*Sqrt[2]*(E^(I*0.4)); 
R = 15; 
L = 0.2; 
eqns = {u1 == Uz, u1 - u2 == R*i, u2 == L*I*ω*i};
Iphasor = i /. Solve[eqns][[1]]; 
itime[t_] := Im[Iphasor*(E^(I*ω*t))];
pl2=Plot[itime[t]/.sol,{t,0,tmax},AxesLabel->{"t [s]","i [A]"},
PlotStyle->{Thick,Black}];
Show[pl1,pl2]