I have a real variable $t$ and a function $f(t)$ giving complex values. How to plot the function for $t$ in a given real interval? Also is there a way to do it in Wolfram Alpha website?
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1 Answer
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ReImPlot[2 t + I t^2, {t, -\[Pi], \[Pi]}]
That is a new built-in in V12 and newer: ReImPlot
ReImPlot[{ArcSin[x], ArcCos[x]}, {x, -4, 4},
PlotLabels -> "Expressions"]
The input that suffices for WolframAlpha is simpler
WolframAlpha["2 t+I t^2 plot -pi to pi"]
WolframAlpha["{ArcSin[x],ArcCos[x]} plot -4 to 4"]
has some unexpected behavior with the desired interval. It does not show the continuation.
An introductory example is
ReImPlot[{Sqrt[1 - x^2], -Sqrt[x^2 - 1]}, {x, -3, 3}]
This separates the branches of roots very neat.
AbsArgPlot[1 + Exp[-Abs[x]] Sin[I Sin[5 x]], {x, -Pi, Pi},
PlotRange -> Full]
AbsArgPlot is an acompanying function suiting the given criteria too.
A Mathematica example is the Nyquist plot:
h = 1/(s - 1/2)^2 /. s -> Exp[I \[Omega]]
ParametricPlot[{Re[h], Im[h]}, {\[Omega], 0, 2 Pi}]
answered Dec 13, 2020 at 21:36
f[t_]:=2 t+I t^2; ParametricPlot[{Re[f[t]],Im[f[t]]},{t,-3,3}]works with Mathematica.ParametricPlot[{Re[2 t+I t^2], Im[2 t+I t^2]},{t,-3,3}]works with WolframAlpha. $\endgroup$ReIm[f[t]]instead of{Re[f[t]], Im[f[t]]}in Mathematica, although it produces the same result and WA seems not to understand it. $\endgroup$