How to plot a function, that is not properly defined in mathematica? [closed]

Question

After rather long and relatively complicated calcuations, I finally got to a point where all my $x(t)$ functions are

equationSolution = {0.015922 + (0.0000570403 - 
     0.000813858 I) C2 E^((-11.2868 - 344.474 I) t) + (0.0000570403 + 
     0.000813858 I) C1 E^((-11.2868 + 344.474 I) t) - (0.00277545 - 
     0.0208373 I) C6 E^((-5.40686 - 40.5931 I) t) - (0.00277545 + 
     0.0208373 I) C5 E^((-5.40686 + 40.5931 I) t) + (1.79914*10^-18 - 
     0.00355291 I) C4 E^((-1.42109*10^-14 - 
      162.498 I) t) + (1.79914*10^-18 + 
     0.00355291 I) C3 E^((-1.42109*10^-14 + 162.498 I) t), 
 0.015922 - (0.0000644748 - 
     0.00196777 I) C2 E^((-11.2868 - 344.474 I) t) - (0.0000644748 + 
     0.00196777 I) C1 E^((-11.2868 + 344.474 I) t) - (0.0016191 - 
     0.00862548 I) C6 E^((-5.40686 - 40.5931 I) t) - (0.0016191 + 
     0.00862548 I) C5 E^((-5.40686 + 
      40.5931 I) t) - (8.57858*10^-19 - 
     0.00355291 I) C4 E^((-1.42109*10^-14 - 
      162.498 I) t) - (8.57858*10^-19 + 
     0.00355291 I) C3 E^((-1.42109*10^-14 + 162.498 I) t), 
 0.015922 - (0.0000644748 - 
     0.00196777 I) C2 E^((-11.2868 - 344.474 I) t) - (0.0000644748 + 
     0.00196777 I) C1 E^((-11.2868 + 344.474 I) t) - (0.0016191 - 
     0.00862548 I) C6 E^((-5.40686 - 40.5931 I) t) - (0.0016191 + 
     0.00862548 I) C5 E^((-5.40686 + 
      40.5931 I) t) + (1.00256*10^-18 - 
     0.00355291 I) C4 E^((-1.42109*10^-14 - 
      162.498 I) t) + (1.00256*10^-18 + 
     0.00355291 I) C3 E^((-1.42109*10^-14 + 162.498 I) t), 
 0.015922 - (0.280997 + 
     0.010463 I) C2 E^((-11.2868 - 344.474 I) t) - (0.280997 - 
     0.010463 I) C1 E^((-11.2868 + 344.474 I) t) + (0.860855 + 
     0. I) C6 E^((-5.40686 - 40.5931 I) t) + (0.860855 + 
     0. I) C5 E^((-5.40686 + 40.5931 I) t) - (0.577339 + 
     1.69348*10^-16 I) C4 E^((-1.42109*10^-14 - 
      162.498 I) t) - (0.577339 - 
     1.69348*10^-16 I) C3 E^((-1.42109*10^-14 + 162.498 I) t), 
 0.015922 + (0.678573 + 
     0. I) C2 E^((-11.2868 - 344.474 I) t) + (0.678573 + 
     0. I) C1 E^((-11.2868 + 344.474 I) t) + (0.358889 + 
     0.0190875 I) C6 E^((-5.40686 - 40.5931 I) t) + (0.358889 - 
     0.0190875 I) C5 E^((-5.40686 + 40.5931 I) t) + (0.577339 + 
     0. I) C4 E^((-1.42109*10^-14 - 162.498 I) t) + (0.577339 + 
     0. I) C3 E^((-1.42109*10^-14 + 162.498 I) t), 
 0.015922 + (0.678573 + 
     8.32667*10^-17 I) C2 E^((-11.2868 - 344.474 I) t) + (0.678573 - 
     8.32667*10^-17 I) C1 E^((-11.2868 + 344.474 I) t) + (0.358889 + 
     0.0190875 I) C6 E^((-5.40686 - 40.5931 I) t) + (0.358889 - 
     0.0190875 I) C5 E^((-5.40686 + 40.5931 I) t) - (0.577339 + 
     2.27914*10^-16 I) C4 E^((-1.42109*10^-14 - 
      162.498 I) t) - (0.577339 - 
     2.27914*10^-16 I) C3 E^((-1.42109*10^-14 + 162.498 I) t)}

Where there are two problems. I can't replace constants C1->C6 with those values

constants = {0.0164507 - 2.02961 I, 0.0164507 + 2.02961 I, 
 2.20498*10^-16 - 1.71741*10^-16 I, 
 2.50228*10^-16 - 1.3643*10^-16 I, -0.0285463 - 
  0.465175 I, -0.0285463 + 0.465175 I}

And I can't plot the functions using

Plot[equationSolution[[1]], {t, 0, 5}]

Anybody has an idea what to do?

I know that normally I should post a working example, but the code is quite long - approximately 100 lines.

Answer 1

You can use Symbol and MapIndexed to create a list of Rules for use in ReplaceAll on equationSolution.

eqs = equationSolution /. MapIndexed[Symbol["C" <> ToString@First@#2] -> #1 &, constants];

Then you can use ReIm in Plot to separate the real and imaginary parts of each equation. PlotStyle is used to give the same colour to each equations real and imaginary part while giving the imaginary part a Dashed line. LineLegend is used as a custom legend.

Plot[Evaluate[ReIm /@ eqs], {t, 0, .3},
 PlotRange -> Full,
 AxesLabel -> {t, None},
 PlotStyle -> (Sequence @@ {Directive[Thin, ColorData[1][#]], 
       Directive[Dashed, ColorData[1][#]]} & /@ Range[Length@eqs]),
 PlotLegends -> Column@{
    LineLegend@*Sequence @@ 
     Transpose[{ColorData[1][#], "Eq. " <> ToString@#} & /@ 
       Range[Length@eqs]],
    LineLegend[{Thin, Dashed}, {"Real", "Imaginary"}]
    },
 ImageSize -> Large]

However, the imaginary parts of the equations are very small so it may be worth plotting these in their own chart or use some of the two y-axis plot methods found here.

Hope this helps.