# How to plot in the complex plane? [duplicate]

I am new to Mathematica and I would like to ask how to plot in the complex plane in general. Also, as an example, how do you plot $e^{i\theta}$ in Mathematica? In physics the function $e^{i\theta}$ is called the wavefunction for a free particle so I also like to plot it in Mathematica as a free particle. Thanks in advance.

## marked as duplicate by MarcoB, bbgodfrey, user9660, dr.blochwave, ubpdqnFeb 8 '16 at 9:38

• Please search this site for similar questions; you could start from this search. – MarcoB Feb 8 '16 at 5:27
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• Thanks. Anyway, I think I stated the problem incompletely. In physics the function $e^{i\theta}$ is called the wavefunction for a free particle. So I also like to plot it in Mathematica as a free particle. – PhilCsar Feb 8 '16 at 5:40

Upon MarcoB's suggestion:

complex[θ_] = Exp[I θ];
ListPlot[Table[ReIm@complex@θ, {θ, 0, 2 Pi, 0.01}],
AspectRatio -> Automatic, Joined -> True]


Example

complex[θ_] = Log@θ Exp[I θ];
ListPlot[Table[ReIm@complex@θ, {θ, 0, 2 Pi, 0.01}],
AspectRatio -> Automatic, Joined -> True]


• Consider using ReIm instead of constructing the list of real, imaginary parts yourself. This would work just fine as well: Plot[ReIm@complex@θ, {θ, 0, 2 Pi}]. – MarcoB Feb 8 '16 at 5:31

A compact approach is

ParametricPlot[ReIm[Log[θ] Exp[I θ]], {θ, 0, 2 Pi}]


producing the same curve that appears in the answer by thedude. It works for any complex function of a single real variable.

Appropriate to the season, a cartiod can be plotted by

ParametricPlot[ReIm[I(Exp[I θ] + 1)^2], {θ, -Pi, Pi}]