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)*References*: <2b6b0211-d5e3-46e5-a3da-7922561809c9@p58g2000hsb.googlegroups.com>

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}]