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.
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1$\begingroup$ Please search this site for similar questions; you could start from this search. $\endgroup$– MarcoBFeb 8, 2016 at 5:27
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1$\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$– bbgodfreyFeb 8, 2016 at 5:39
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$\begingroup$ 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. $\endgroup$– anonymousFeb 8, 2016 at 5:40
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2 Answers
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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]
answered Feb 8, 2016 at 5:28
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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}]
answered Feb 8, 2016 at 5:50