Solve[z^5==30,z]

(* Poniższe definicje MyArg, MyRoot i MyRootv2 pochodzą z wykładu NOF_3.nb *)

MyArg[z_]:=If[Arg[z]≥0,Arg[z],Arg[z]+2*Pi]

MyRoot[n_,z_]:=Table[(Abs[z])^(1/n)*Exp[I*(MyArg[z]+2*k*Pi)/n],{k,0,n-1,1}]

MyRootv2[n_,z_]:=Table[(Abs[z])^(1/n)*(Cos[(MyArg[z]+2*k*Pi)/n]+I*Sin[(MyArg[z]+2*k*Pi)/n]),{k,0,n-1,1}]

MyRoot[5,30]

p=MyRootv2[5,30]

pkty=Table[{Re[p[[i]]],Im[p[[i]]]},{i,1,Length[p]}]

pl1=ListPlot[pkty,AspectRatio->1,AxesLabel->{"x","y"},PlotStyle->{Red,PointSize[Large]},PlotRange->{{-2.5,2.5},{-2.5,2.5}}]

pl2=ContourPlot[x^2+y^2==30^(2/5),{x,-2.5,2.5},{y,-2.5,2.5}];

Show[pl1,pl2]

ClearAll[p,pkty,pl1,pl2];

MyRoot[5,30+12*I]

p=MyRootv2[5,30+12*I]

pkty=Table[{Re[p[[i]]],Im[p[[i]]]},{i,1,Length[p]}]

pl1=ListPlot[pkty,AspectRatio->1,AxesLabel->{"x","y"},PlotStyle->{Red,PointSize[Large]},PlotRange->{{-2.5,2.5},{-2.5,2.5}}]

r=(6^(1/5)) (29^(1/10));

pl2=ContourPlot[x^2+y^2==r^2,{x,-2.5,2.5},{y,-2.5,2.5}];

Show[pl1,pl2]