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Re: Complex solutions to simple equations


On 11=E6=9C=887=E6=97=A5, =E5=8D=88=E5=BE=8C8:48, dragonman <morrisneedle.. . at gmail.com> wrote:
> I want the solutions to x^n=1 to appear in the form r(cos theta +isin
> theta) and then to graph them on an Argand diagram. Any advice given
> would be much appreciated.

RootPlotStyle[poly_, z_] :=
  ListPlot[{Re[z], Im[z]} /.
     NSolve[poly == 0, z], AspectRatio ->
     Automatic, PlotStyle ->
     {PointSize[0.06], Hue[0.8521]}] /;
   PolynomialQ[poly, z]

n = 7;
poly = z^n - 1;
sol = Solve[poly == 0, z] /.
    (a_ -> b_) :> a -> ComplexExpand[b];
z /. sol
RootPlotStyle[poly, z]

n = 24;
poly = z^n - 1;
sol = Solve[poly == 0, z] /.
    (a_ -> b_) :> a -> ComplexExpand[b];
TableForm[z /. sol]
RootPlotStyle[poly, z]


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