I don't know how to plot the exponential of an imaginary number. The function I've to plot is: Exp[-I w t]. I can give w a number, so I've chose w=1 and:
Plot [E^ [-I t], {t, -20, 20}]
but it shows nothing.
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1 Answer
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The old school way is to plot the Re and Im part separately. Or you can plot them parametrically as @LouisB suggested.
f[t_] = Exp[-I t]
Plot[{Re[f[t]], Im[f[t]]}, {t, -20, 20}]
ParametricPlot[{Re[f[t]], Im[f[t]]}, {t, -20, 20}, AxesLabel -> {"Re", "Im"}]
If you are using V12, then you can use ReImPlot
ReImPlot[f[t], {t, -20, 20}]
ReImPlot[Exp[-I t], {t, -20, 20}]orReImPlot[E^(-I t), {t, -20, 20}]? $\endgroup$Exp[I t]as a function of t is a number on the unit circle. With increasing t, the number circulates clockwise around the origin. AndExp[-I t]anti clockwise. Therefore plottingReImgivesSinandCosfunctions oft. $\endgroup$ParametricPlot[ReIm@Exp[I t], {t, 0, 2 \[Pi]}]to obtain an Argand diagram of $e^{i t}$. $\endgroup$