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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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    $\begingroup$ try ReImPlot[Exp[-I t], {t, -20, 20}] or ReImPlot[E^(-I t), {t, -20, 20}]? $\endgroup$ – kglr Feb 26 at 19:01
  • $\begingroup$ 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. And Exp[-I t] anti clockwise. Therefore plotting ReIm gives Sinand Cos functions of t. $\endgroup$ – Daniel Huber Feb 26 at 19:30
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    $\begingroup$ Use ParametricPlot[ReIm@Exp[I t], {t, 0, 2 \[Pi]}] to obtain an Argand diagram of $e^{i t}$. $\endgroup$ – LouisB Feb 27 at 6:11
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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"}] 

enter image description here

If you are using V12, then you can use ReImPlot

ReImPlot[f[t], {t, -20, 20}]

enter image description here

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