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MathGroup Archive 2005

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Re: Solutions of an equation under complex form

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54529] Re: [mg54478] Solutions of an equation under complex form
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Tue, 22 Feb 2005 04:24:00 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200502210844.DAA27204@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

In such situations, ComplexExpand is your friend!  Thus:

   Solve [x^2 + x + 1 == 0, x]
   ComplexExpand[x /. %]  // InputForm
{-(1/2) - (I*Sqrt[3])/2, -(1/2) + (I*Sqrt[3])/2}



Michaël Monerau wrote:
> Hello,
> 
> I'm running into a little problem under Mathematica 5.0 but I'm sure 
> people here will just take it as "too easy", but, well :) I just want 
> the solutions of the equation :
> 
> x^2 + x + 1 == 0
> 
> under their complex form.
> 
> So, I type :
> 
> Solve [x^2 + x + 1 == 0, x]
> 
> But I unfortunately get :
> { { {x -> -(-1)^(1/3) }, { x -> (-1)^(2/3) } } }
> 
> And I'd prefer to obtain the more "readable" form :
> -1/2 + I*1/2*Sqrt[3], -1/2 - I*1/2*Sqrt[3]
> 
> that I would get under another system for instance. What special function
> should I call to get this form under Mathematica ?
> 
> Thanks for any help

-- 
Murray Eisenberg                     murray at 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



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