Thank you for your cooperation.
Folks take a note of the new M10.1 function ReIm. With it code becomes simpler:
ParametricPlot[ReIm[Sqrt[E^(-7 I t)] + E^(I t)], {t, -2, 5}, Exclusions -> None]
Simon Cadrin, I suggest reading about proper posting of code on this website. It is easier for those who help you to copy code from your post. Equations in images are strongly discouraged.
The trick to getting the vertical lines is to use Exclusions -> None as a plot option:
zr[t_] := Re[Sqrt[E^(-7 I t)] + E^(I t)] zi[t_] := Im[Sqrt[E^(-7 I t)] + E^(I t)] ParametricPlot[{zr[t], zi[t]}, {t, -2, 5}, MaxRecursion -> 10, Exclusions -> None]
a beautiful presentation ...
See attached notebook.
How to plot this new curve ?
Try these 3D plots:
Plot3D[Re[E^(x + I y)], {x, 0, 2 Pi}, {y, 0, 2 Pi}, PlotRange -> All] Plot3D[Im[E^(x + I y)], {x, 0, 2 Pi}, {y, 0, 2 Pi}, PlotRange -> All]
ParametricPlot[{Re[Exp[I t]], Im[Exp[I t]]}, {t, 0, 2 Pi}]
