# roots of unity Visualization

Posted 8 years ago
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 Hey there,I'm a german student and very new here. Wikipedia brought me here because of a skilled work in mathematics. It's about visualizing roots of unity and I found a graphic made with wolfram mathematica: https://de.wikipedia.org/wiki/Einheitswurzel#/media/File:Complex_x_hoch_5.jpgIt would be very pretty if I could visualize my roots of unity in a similar way. I have already visualized the unity roots in a coordinate system but don't know how to colorize it like wikipedia's one. Maybe with the colorschemes but I don't know how to put them in my already written input. I added a file of my already written one and hope it works.Maybe someone can help me. It would be very great.Thank you. Attachments:
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Posted 8 years ago
 Here it is: Show[DensityPlot[Sin[3 Arg[(x + I y)^3 - 1]], {x, -2, 2}, {y, -2, 2}, ColorFunction -> "Rainbow", Exclusions -> None, PlotPoints -> 61], ListPlot[Table[{Re[E^(I*2 \[Pi]*n/12)], Im[E^(I*2 \[Pi]*n/12)]}, {n, 0, 20}], AspectRatio -> Automatic, PlotStyle -> {{ Black, PointSize[.02]}}], Table[ Graphics [{Thick, Dashed, Black, Line[{{Re[E^(I*2 \[Pi]*n/12)], Im[E^(I*2 \[Pi]*n/12)]}, {Re[E^(I*2 \[Pi]*(n + 1)/12)], Im[E^(I*2 \[Pi]*(n + 1)/12)]}}]}], {n, 0, 20}]] 
Posted 8 years ago
 thx
Posted 8 years ago
 Yes, you can overlay a DensityPlot and your original plot with Show[plot1,plot2]. Be careful of the order: plot1 is at the bottom, plot2 is on top.
Posted 8 years ago
 Yeah this looks really good. But couldn't I plot those colors in my already written input?Thanks a lot.
Posted 8 years ago
 I get something vaguely similar with DensityPlot[Sin[3 Arg[(x + I y)^3 - 1]], {x, -2, 2}, {y, -2, 2}, ColorFunction -> "Rainbow"] I don't quite understand it, though.
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