Complex Numbers

[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)

[Hootenanny]

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.

[m_s_a]

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.

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

[Dick]

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)

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.

[Hootenanny]

Take note that (x+iy)(x+iy) is NOT equal to x^2-y^2. It's x^2-y^2+2ixy.
Nice catch Dick, didn't even see it :redface:

[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:confused:
Thanks

[Hootenanny]

But this is a question in one of the issues:confused:
Then I would suggest that,

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

[m_s_a]

Then I would suggest that,

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

Thank you a lot