- 91
- 0
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)
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)
Thank you for you on your responseIt 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.
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.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)
Nice catch Dick, didn't even see itTake note that (x+iy)(x+iy) is NOT equal to x^2-y^2. It's x^2-y^2+2ixy.
Then I would suggest that,But this is a question in one of the issues
Thank you a lotThen I would suggest that,
[tex]z^2 = x^2 +2ixy - y^2[/tex]