# Complex Numbers

1. Apr 16, 2008

### m_s_a

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. Apr 16, 2008

### Hootenanny

Staff Emeritus
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.

3. Apr 16, 2008

### m_s_a

Thank you for you on your response
And on the new information for me

4. Apr 16, 2008

### Dick

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.

5. Apr 16, 2008

### Hootenanny

Staff Emeritus
Nice catch Dick, didn't even see it

6. Apr 16, 2008

### m_s_a

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
Thanks

7. Apr 16, 2008

### Hootenanny

Staff Emeritus
Then I would suggest that,

$$z^2 = x^2 +2ixy - y^2$$

8. Apr 16, 2008

### m_s_a

Thank you a lot