       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)/2, -(1/2) + (I*Sqrt)/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, -1/2 - I*1/2*Sqrt
>
> 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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