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Subfield of the field of complex numbers

  1. Feb 6, 2010 #1
    Can anyone prove to me why each subfield of the field of complex numbers contains every rational numers?
     
    Last edited: Feb 6, 2010
  2. jcsd
  3. Feb 6, 2010 #2

    Hurkyl

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    Hrm. Let's start with a simpler question: can you say why they must all contain the number 2? What other numbers can you say something about?
     
  4. Feb 6, 2010 #3

    HallsofIvy

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    Any subfield of the complex numbers must include 0 and 1. Since it is closed under addition, it must include every positive integer. Since it has additive inverses, it must include every negative integer. Since every member except 0 has a multiplicative inverse, ....
     
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