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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93016] How does Mathematica know whether a number is real or complex?
  • From: Peng Yu <PengYu.UT at gmail.com>
  • Date: Fri, 24 Oct 2008 02:27:34 -0400 (EDT)

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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