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Comples Numbers

  1. Mar 7, 2010 #1
    Complex Numbers

    Hello,

    Why when dealing with complex numbers, as with multiplication, we use the complex conjugate operator?

    Regards
     
    Last edited: Mar 7, 2010
  2. jcsd
  3. Mar 7, 2010 #2
    So we can do complex 'division' and fractions.

    Compare what happens in the following

    [tex]\frac{{a + ib}}{{c + id}}*\frac{{c - id}}{{c - id}}[/tex]

    with

    [tex]\frac{{a + ib}}{{c + id}}*\frac{{c + id}}{{c + id}}[/tex]
     
  4. Mar 7, 2010 #3
    Re: Complex Numbers

    I didn't get it. I mean, in telecommunication systems, when we deal with baseband signals, we deal with complex numbers, and all the time we use the complex conjugate operator, but I don't understand why and what it is mean physically.
     
  5. Mar 7, 2010 #4
    I did expect you to work my examples out.

    Which one contained the conjugate and which one leads to a single complex number result?

    If you apply a formula in real analysis say 27*3 you want the simple answer 81, not something more difficult than you started with such as

    [tex]{\left( {\sqrt 9 } \right)^2}*{\left( {\sqrt 9 } \right)^2}[/tex]

    The same is true of complex numbers.

    What does simple multiplication by a conjugate yield by the way ( a real number)?
     
  6. Mar 7, 2010 #5

    HallsofIvy

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    Science Advisor

    The product of a complex number and its conjugate has the nice property that is a real number- and for any z other than 0 [math]z*\overline{z}[/math] is a positive real number.
     
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