# Complex Numbers

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)

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Hootenanny
Staff Emeritus
Gold Member
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.

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
Homework Helper
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
Staff Emeritus
Gold Member
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

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

Hootenanny
Staff Emeritus
Gold Member
But this is a question in one of the issues
Then I would suggest that,

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

Then I would suggest that,

$$z^2 = x^2 +2ixy - y^2$$
Thank you a lot