       Re: Complex solutions to simple equations

• To: mathgroup at smc.vnet.net
• Subject: [mg104769] Re: Complex solutions to simple equations
• From: ynb <wkfkh056 at yahoo.co.jp>
• Date: Mon, 9 Nov 2009 05:45:22 -0500 (EST)
• References: <hd3mr5\$9pv\$1@smc.vnet.net>

```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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