Clear[sig];
Clear[omega];
Clear[x];


Manipulate[
Table[
{
Plot[{Exp[-sigma z] Cos[omegaa z],Exp[-sigma z] Sin[omegaa z]},{z,0,10},PlotRange -> {-1.1,1.1},PlotStyle-> {RGBColor[1,0,0],RGBColor[0,0,1]},ImageSize->{500,400}],
Plot[{ Exp[-sigma z]  ,ArcTan[Cos[omegaa z],Sin[omegaa z]]},{z,0,10},PlotRange -> {-1.1 Pi,1.1 Pi},PlotStyle-> {RGBColor[0,1,0],RGBColor[1,0,1]},ImageSize->{500,400}]}], 
{ {sigma,0,"sigma"},-1,2},
{ {omegaa,4,"omega"},-10,10} ]