# Why Does Mathematica Have Trouble Plotting This?

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: mathematica.stackexchange.com/questions/3458/… – Michael E2 Jul 27 '18 at 18:08

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"}
] • @rhermans Many thanks – Brandon Jul 26 '18 at 18:11