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    $\begingroup$ ParametricPlot has the attribute HoldAll. I suspect you will get the result you want by wrapping Evaluate around the first argument to ParametricPlot. $\endgroup$ Commented Aug 23, 2016 at 17:53
  • $\begingroup$ We don't have your definition of z, but here's an example of what chuy is talking about, using another complex function: i.sstatic.net/QX56X.png $\endgroup$ Commented Aug 23, 2016 at 17:55