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I have a list with complex numbers and I want to animate them. How can i do this? I would like to have appearing lines between points. I hope you know what I mean. Here is my code:

 roots[re_, im_, n_] := 
     Module[{a = re, b = im, zkList, phi, zk, k, IM, RE, zkList2, p, 
       number},
      number = a + I*b;
      zkList = 
       Table[{Power[Abs[re + im*I], (
           n)^-1]*(Cos[(Arg[re + im*I] + 2*k*Pi)/n]) + 
          I*Sin[(Arg[re + im*I] + 2*k*Pi)/n]}, {k, 0, n - 1}];
        zkList]

Example:

roots[1, 0, 4]
{1, I, -1, -I}
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  • $\begingroup$ It's not clear what you're asking. Lines between what points? $\endgroup$ – MelaGo Oct 24 '19 at 23:48
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I am not sure I understand what is the aim. I post this as motivation. Apologies for errors and misunderstanding. Manipulate andDynamicModule are useful for dynamic/interactive exploration. Locator can allow you to explore different z. Slider2D can also be useful.

Here is an example: 

Manipulate[
 Module[{r = Norm[pt]^(1/n), pts}, 
  pts = Table[
    r {Cos[ArcTan @@ pt/n + 2 Pi j/n], 
      Sin[ArcTan @@ pt/n + 2 Pi j/n]}, {j, 0, n - 1}]; 
  Graphics[{Point[pt], Red, PointSize[0.03], Point[pts], Blue, 
    Circle[{0, 0}, Norm[pt]], Orange, FaceForm[None], 
    EdgeForm[Orange], Polygon[pts], Circle[{0, 0}, r], Black, 
    Line[{{0, 0}, #}] & /@ pts, Circle[{0, 0}, 1]}, Frame -> True, 
   PlotRange -> {{-3, 3}, {-3, 3}}]], {{pt, {1, 0}}, Locator}, {n, 
  Range[2, 7]}]

enter image description here

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  • $\begingroup$ ‘Here’? Is that meant to be a hyperlink? I am happy to delete my answer. $\endgroup$ – ubpdqn Oct 25 '19 at 9:15
  • $\begingroup$ Hello, thank for your post. Here is what I meant. 'Animate[ListPlot[zkList[[1 ;; i]], PlotMarkers -> {Automatic, Small}, Joined -> True, PlotRange -> {{-2, 2}, {-2, 2}}], {i, 1, n, 1}]' Unfortunately, it does not show line between first and last point. Do you know how to fix this? $\endgroup$ – Janukalado Oct 25 '19 at 9:17
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    $\begingroup$ @Janukalado you could just modify your Table from 0 to n to repeat the first element and allow closure. Otherwise use Graphics and Polygon. $\endgroup$ – ubpdqn Oct 25 '19 at 9:20

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