Plot3D[{((Abs[x+I y])^3)Arg[(x+I y)^8]/5,2+((Abs[x+I y])^3)Arg[(E^(π I/2))(x+I y)^8]/5},{x,-1,1},{y,-1,1}, Exclusions->None, RegionFunction->((((#1)^2)+((#2)^2))<1&)]

Plot3D[{((Abs[x+I y])^3)Arg[(x+I y)^2]/3,2+((Abs[x+I y])^3)Arg[(E^(π I/2))(x+I y)^3]/2},{x,-1,1},{y,-1,1}, Exclusions->None, RegionFunction->((((#1)^2)+((#2)^2))<1&)]

((Abs[x+I y])^3)/.{x->Sin[t],y->Cos[t]}//Simplify

r Cos[t]+r I Sin[t]

TrigToExp[r Cos[t]+I r Sin[t]]

TrigToExp[I Cos[t]+Sin[t]]

TrigReduce[I Cos[t]+Sin[t]]

TrigToExp[I (Cos[t]-I Sin[t])]

Table[2k+((Abs[x+I y])^3)Arg[(E^(k π I/2))(x+I y)^2]/3, {k,0,3}]

(1/3) ((Abs[x+I y])^3) Arg[(((x+I y))^2)]/.{x->Cos[θ],y->Sin[θ]}

TrigToExp[(1/3) ((Abs[Cos[t]+I Sin[t]])^3) Arg[(((Cos[t]+I Sin[t]))^2)]]

Plot3D[Table[2k+((Abs[x+I y])^3)Arg[(E^(k π I/2))(x+I y)^2]/3, {k,0,4}],{x,-1,1},{y,-1,1}, Exclusions->None, RegionFunction->((((#1)^2)+((#2)^2))<1&),BoxRatios->{1,1,2}]

knot=ParametricPlot3D[{{Sin[((3 θ)/2)],Cos[((3 θ)/2)],((2 n π)/3)+θ},{-Sin[((3 θ)/2)],-Cos[((3 θ)/2)],((2 n π)/3)+θ}}/.n->0,{θ,0,2π},PlotStyle->{Thick,Blue}];

Show[
knot,
ParametricPlot3D[Table[{r Sin[θ],r Cos[θ],π n+(1/3) ((Abs[x+I y])^3) Arg[Exp[n I π](((x+I y))^2)]/.{x->r Cos[θ],y->r Sin[θ]} },{n,0,2}],{θ,0,2Pi},{r,0,1},PlotPoints->50,Exclusions->None]
]

knot=ParametricPlot3D[{{Sin[((3 θ)/2)],Cos[((3 θ)/2)],((2 n π)/3)+θ},{-Sin[((3 θ)/2)],-Cos[((3 θ)/2)],((2 n π)/3)+θ}}/.n->0,{θ,0,2π},PlotStyle->{Thick,Blue}]

Show[
knot,
ParametricPlot3D[Table[{r Sin[θ],r Cos[θ],π n+(1/3) ((Abs[x+I y])^3) Arg[Exp[n I π](((x+I y))^2)]/.{x->Cos[θ],y->Sin[θ]} },{n,0,2}],{θ,0,2Pi},{r,0,1},PlotPoints->50]
]

ParametricPlot3D[{{((2 n π)/3)+θ,Sin[((3 θ)/2)],Cos[((3 θ)/2)]},{((2 n π)/3)+θ,-Sin[((3 θ)/2)],-Cos[((3 θ)/2)]}}/.n->0,{θ,0,2π}]