Manipulate[ComplexPlot[z^4+1/z^4,
{z,-1.4-1.4 I,1.4+1.4 I},ColorFunction->colfun,ImageSize->500],
{colfun,{"CyclicLogAbs","CyclicLogAbsArg",
"ShiftedCyclicLogAbs","CyclicReImLogAbs"}}]
DensityPlot[Arg[(x+I y)^4+1/(x+I y)^4],
{x,-1.4,1.4},{y,-1.4,1.4},PlotPoints->200,
ColorFunction->(Hue[#/(2 Pi)] &),
ColorFunctionScaling->False,ImageSize->500]
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