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Mathematica's special technique for handling complex values in a plot is to simply ignore them -- it plots nothing for at values of the domain for which the range is complex. Experiment with the following code. Manipulate[ PolarPlot[r[t], {t, min °, max °}, PlotRange -> {{0, 3.5}, {-1.5, 1.5}}, PlotRangePadding -> Scaled[.05], Epilog ...

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