Re: Re: Complex solutions to simple equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg104785] Re: [mg104769] Re: Complex solutions to simple equations*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Tue, 10 Nov 2009 05:57:42 -0500 (EST)*References*: <hd3mr5$9pv$1@smc.vnet.net> <200911091045.FAA05651@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

RootPlotStyle cuts off some points at the edges of the plot, so I'll suggest a small improvement or two. RootPlotStyle[poly_, z_, ptsize_] := Module[{pts = {Re[z], Im[z]} /. NSolve[poly == 0, z], limits}, limits = (ptsize {-1, 1} + Through[{Min, Max}@#]) & /@ Transpose@pts; ListPlot[pts, AspectRatio -> Automatic, PlotStyle -> {PointSize[ptsize], Hue[0.8521]}, PlotRange -> limits] ] /; PolynomialQ[poly, z] n = 7; poly = z^n - 1; sol = Solve[poly == 0, z] /. (a_ -> b_) :> a -> ComplexExpand[b]; z /. sol RootPlotStyle[poly, z, .06] and n = 24; poly = z^n - 1; sol = Solve[poly == 0, z] /. (a_ -> b_) :> a -> ComplexExpand[b]; Grid@Partition[z /. sol // Simplify, 4] RootPlotStyle[poly, z, .06] Bobby On Mon, 09 Nov 2009 04:45:22 -0600, ynb <wkfkh056 at yahoo.co.jp> wrote: > 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] > -- DrMajorBob at yahoo.com

**References**:**Re: Complex solutions to simple equations***From:*ynb <wkfkh056@yahoo.co.jp>