1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Comples Numbers

  1. Mar 7, 2010 #1
    Complex Numbers


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

    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]


    [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


    User Avatar
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook