- #1
m_s_a
- 88
- 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)
Hootenanny said: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 said: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 itDick said:Take 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,m_s_a said:But this is a question in one of the issues
Hootenanny said:Then I would suggest that,
[tex]z^2 = x^2 +2ixy - y^2[/tex]
Complex numbers are numbers that consist of a real part and an imaginary part. The real part is a normal number that we are familiar with, while the imaginary part is a multiple of the imaginary unit, which is denoted by i and is equal to the square root of -1.
Complex numbers are often represented in the form of z = x + iy, where x is the real part and y is the imaginary part. This is known as the standard form of a complex number.
Complex numbers can be visualized in the Cartesian plane, with the real part representing the horizontal axis and the imaginary part representing the vertical axis. The point (x,y) in the Cartesian plane corresponds to the complex number z = x + iy.
To perform addition, subtraction, and multiplication on complex numbers, we simply combine the real parts and the imaginary parts separately. For division, we use the conjugate of the denominator to rationalize the expression.
When we multiply two complex numbers, we are essentially scaling and rotating them on the complex plane. The modulus (or magnitude) of the product is equal to the product of the moduli of the two complex numbers, and the argument (or angle) of the product is equal to the sum of the arguments of the two complex numbers.