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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 (MichaÃ«l 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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