# Animating roots of complex numbers

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}

• It's not clear what you're asking. Lines between what points? – MelaGo Oct 24 '19 at 23:48

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]}] • ‘Here’? Is that meant to be a hyperlink? I am happy to delete my answer. – ubpdqn Oct 25 '19 at 9:15
• 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? – Janukalado Oct 25 '19 at 9:17
• @Janukalado you could just modify your Table from 0 to n to repeat the first element and allow closure. Otherwise use Graphics and Polygon. – ubpdqn Oct 25 '19 at 9:20