Comples Numbers

  • Thread starter EngWiPy
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  • #1
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Main Question or Discussion Point

Complex Numbers

Hello,

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

Regards
 
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Answers and Replies

  • #2
5,439
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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]
 
  • #3
1,367
61


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]
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.
 
  • #4
5,439
7
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)?
 
  • #5
HallsofIvy
Science Advisor
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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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