       Re: How does Mathematica know whether a number is real or complex?

• To: mathgroup at smc.vnet.net
• Subject: [mg93026] Re: How does Mathematica know whether a number is real or complex?
• From: "Peng Yu" <pengyu.ut at gmail.com>
• Date: Fri, 24 Oct 2008 02:29:29 -0400 (EDT)

```Hi,

I haven't seen this message posted on the newsgroup. Is it not
appropriate for the newsgroup?

Thanks,
Peng

On Wed, Oct 22, 2008 at 11:18 AM, Peng Yu <PengYu.UT at gmail.com> wrote:
> Hi,
>
> The solution of the equation at the end of this post is
>
> {{x -> -0.9702291184141268, y -> -0.24218888864137905},
>  {x -> -0.44830718122625973, y -> 0.8938795619438703},
>  {x -> 1.3776284630851778 - 0.7866963118457873*I,
>  y -> -0.9763348915886718 - 1.1100445557562666*I},
>  {x -> 1.3776284630851778 + 0.7866963118457873*I,
>  y -> -0.9763348915886718 + 1.1100445557562666*I}}
>
> Two of the solutions are real. The other two are complex.
>
> I'm wondering how Mathematica know whether a solution is real or
> complex.
> If a solution actually has a close-to-zero imaginary part, will
> mathematica incorrect consider it as a real number?
>
> Thanks,
> Peng
>
> AA = {{0.45236, -0.241371}, {-0.241371, 0.173649}};
> BB = {-0.500298, 0.141347};
> CC = -0.773749;
> Solve[{{x, y}.AA.{x, y} + BB.{x, y} + CC == 0, x^2 + y^2 == 1}, {x, y}]

```

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