Re: Solutions of an equation under complex form

• To: mathgroup at smc.vnet.net
• Subject: [mg54498] Re: Solutions of an equation under complex form
• From: Peter Pein <petsie at arcor.de>
• Date: Tue, 22 Feb 2005 04:22:56 -0500 (EST)
• References: <cvc7un\$qqr\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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

x /. Solve[x^2 + x + 1 == 0, x] // ComplexExpand
==>
{-(1/2) - (I*Sqrt[3])/2, -(1/2) + (I*Sqrt[3])/2}
--
Peter Pein
Berlin

```

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