Why Does Mathematica Have Trouble Plotting This?

Question

I'm trying to Plot something relatively simple:

Manipulate[
 Plot[Ωm*E^(I*(J - Ωm)*t), {t, 0, 100}, 
  ImageSize -> Large], {J, 1, 100}, {Ωm, 10, 100}]

But Mathematica just returns a blank plot of the first quadrant. I figure that it might be because I'm using a complex exponential (although it's never been a problem before), but I just wanted to make sure

use Re[\[CapitalOmega]m*E^(I*(J - \[CapitalOmega]m)*t)] or Im[\[CapitalOmega]m*E^(I*(J - \[CapitalOmega]m)*t)] as the first argument in Plot? — kglr, Jul 26 '18 at 17:25
Possible duplicate: https://mathematica.stackexchange.com/questions/3458/plotting-complex-quantity-functions — Michael E2, Jul 27 '18 at 18:08

score 4 · Accepted Answer · edited Jul 26 '18 at 18:15

4

Because you are trying to plot a complex number. You can separate Real and Imaginary parts with ReIm

Manipulate[
 Plot[
  Evaluate@ReIm[
    Ωm*E^(I*(J - Ωm)*t)
    ]
  , {t, 0, 100}
  , ImageSize -> Large
  , PlotRange -> {-102, 102}
  , PlotStyle -> Opacity[0.7]
  , PlotPoints -> 100
  , MaxRecursion -> 10
  , PlotLegends -> {Re, Im}
 ]
 , {{J, 49}, 1, 100, 1, Appearance -> "Labeled"}
 , {{Ωm, 50}, 10, 100, 1, Appearance -> "Labeled"}
 ]

edited Jul 26 '18 at 18:15

Bob Hanlon

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answered Jul 26 '18 at 17:28

rhermans

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@rhermans Many thanks – Brandon Jul 26 '18 at 18:11

Why Does Mathematica Have Trouble Plotting This?

1 Answers1