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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: [mg54549] Re: Solutions of an equation under complex form
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Tue, 22 Feb 2005 04:25:38 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 2/21/05 at 3:44 AM, mmonerau at gmail.com (Michaël Monerau) wrote:

>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 ?


Use ComplexExpand, i.e.,

In[1]:=
Solve[x^2 + x + 1 == 0, x]
Out[1]=
{{x -> -(-1)^(1/3)}, {x -> (-1)^(2/3)}}

In[2]:=
(ComplexExpand[x /. #1] & ) /@ %
Out[2]=
{-(1/2) - (I*Sqrt[3])/2,  -(1/2) + (I*Sqrt[3])/2}

And if you have the defualt output set to TraditionalForm, this is even more readable
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