Trying out the complex function feature in mathematica and graphing a function with vectors indicated

complex-function-with-polya-field.wls

 With[{
  limit = 2,
  f = Function[z, z^3 - z]
  },
 Show[{
   ComplexPlot[f[z]
    , {z, limit + limit I, -limit - limit I}
    , Mesh -> {Range[-10, 10, .5], Range[-10, 10, .5]}
    , MeshFunctions -> {Re[#2] &, Im[#2] &}
    , MeshStyle -> {White, Black}
    , PlotPoints -> 100
    , PlotTheme -> "Business"
    , PlotLegends -> Automatic
    ],
   StreamPlot[ReIm[f[x + I y]], {x, -limit, limit}, {y, -limit, limit}]
   }]
 ]