pts=({Re@#,Im@#}&/@(x/.Solve[x^3==27 I]))

Show[ContourPlot[Abs[(x+I y)^3-27 I],{x,-4,4},{y,-4,4},Contours->15],Graphics[{{Style[Text[#,#],17]&/@#},{Opacity[.5],Orange,Thickness[.01],Arrow[{{0,0},#}]&/@#},{Red,PointSize[.02],Point@#}},Axes->True,Frame->True,PlotRangePadding->1,AspectRatio->Automatic]&@pts]

Show[ContourPlot[Arg[(x+I y)^3-27 I],{x,-4,4},{y,-4,4},Contours->15,ColorFunction->"Rainbow"],Graphics[{{Style[Text[#,#],17]&/@#},{Opacity[.5],Orange,Thickness[.01],Arrow[{{0,0},#}]&/@#},{Red,PointSize[.02],Point@#}},Axes->True,Frame->True,PlotRangePadding->1,AspectRatio->Automatic]&@pts]