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From: dragonman on 7 Nov 2009 06:48
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.

From: Mark McClure on 8 Nov 2009 06:51
On Sat, Nov 7, 2009 at 6:49 AM, dragonman <morrisneedleman(a)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.

Here are the solutions to such an equation in
the form you want.
sols = ExpToTrig[z /. Solve[z^99 == 1, z]]

And here they are in the plane.
ListPlot[Table[{Re[z], Im[z]}, {z, sols}],
AspectRatio -> Automatic]

Mark McClure

From: Murray Eisenberg on 8 Nov 2009 06:51
My Mathematica notebook

nthRoots.nb

may help you. You can download it from the Files page at my web site:

http://www.math.umass.edu/~murray/Math_421_Eisenberg/

For its graphics, that notebook relies upon David Park's "Presentations"
Mathematica application. In case that's not available to you, on that
same Files page I have a pdf version of the evaluated notebook.

dragonman 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.
>

--
Murray Eisenberg murray(a)math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305

From: David Bailey on 8 Nov 2009 07:10
dragonman 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.
>
Didn't your teacher tell you how to do this, or give you a reading list?

This board is not here to answer homework questions - what would be the
point?

David Bailey
http://www.dbaileyconsultancy.co.uk

From: ynb on 9 Nov 2009 05:45
On 11=E6=9C=887=E6=97=A5, =E5=8D=88=E5=BE=8C8:48, dragonman <morrisneedle.. .@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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