- #1

- 1,367

- 61

## Main Question or Discussion Point

**Complex Numbers**

Hello,

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

Regards

Last edited:

- Thread starter EngWiPy
- Start date

- #1

- 1,367

- 61

Hello,

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

Regards

Last edited:

- #2

- 5,439

- 7

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

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.

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

- 5,439

- 7

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

Homework Helper

- 41,833

- 955

- Last Post

- Replies
- 12

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 2K

- Replies
- 3

- Views
- 4K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 18

- Views
- 3K

- Last Post

- Replies
- 8

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 10

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 988