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Complex Numbers

  1. Apr 16, 2008 #1
    hi,








    let
    z=x+iy

    z^2=z.zpar=(x+iy)(x-iy)=x^2+y^2
    or
    z^2=(x+iy)(x+iy)=(x^2-y^2)
     
  2. jcsd
  3. Apr 16, 2008 #2

    Hootenanny

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    It very much depends on your field. Generally in mathematics when one says the 'square' of a complex number one means literally multiplication by itself as in your latter example. However, physicists working in QM often refer to the multiplication of a complex number by it's complex conjugate as 'squaring' it, as for your former example.
     
  4. Apr 16, 2008 #3
    Thank you for you on your response
    And on the new information for me
     
  5. Apr 16, 2008 #4

    Dick

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    Take note that (x+iy)(x+iy) is NOT equal to x^2-y^2. It's x^2-y^2+2ixy. Your first 'z^2' is the modulus (size) of the complex number squared. The second is the complex function z*z. They are quite different. A physicist who refers to the first operation as 'squaring' is being pretty sloppy. The proper term is 'modulus squared' and the proper notation is |z|^2.
     
  6. Apr 16, 2008 #5

    Hootenanny

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    Nice catch Dick, didn't even see it :redface:
     
  7. Apr 16, 2008 #6
    Thank you for you on the note:yuck:
    And thank you on the information that you presented
    But this is a question in one of the issues:confused:
    Thanks
     
  8. Apr 16, 2008 #7

    Hootenanny

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    Then I would suggest that,

    [tex]z^2 = x^2 +2ixy - y^2[/tex]
     
  9. Apr 16, 2008 #8
    Thank you a lot
     
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