<< Algebra`ReIm`;

zrej[z_] := z /: Im[z] = 0;
realne = {r, R, X, ω, U};
zrej /@ realne;
Z = I*X + r + R;
proud = (U/Z);
ParametricPlot[{-Im[proud], Re[proud]} /. {r -> 1, 
            X -> 10, U -> 1}, {R, 0, 10000}, 
        AspectRatio -> Automatic, PlotRange -> All, 
        PlotPoints -> 1000, 
        AxesLabel -> {"-Im[I]", "Re[I]"}, 
        PlotStyle -> {Hue[0.6], 
            Thickness[0.008]}];

absIkv = FullSimplify[Im[proud]^2 + Re[proud]^2]

cosfi = FullSimplify[Re[proud]/(Sqrt[absIkv]), U > 0]