# The probability as an absolut value of the square of the amplitude

1. Aug 17, 2010

### TubbaBlubba

All right, I don't have a problme with the concept, just a specific question.

Is the absolute value of the amplitude abs(r^2 + (xi)^2) or abs(r^2) + abs((xi)^2)

Or, to put it in a simpler way - Do you absolute the value of the square of the imaginary part?

The difference would be, say

2^2 + (5i)^2 = 4 + (-25) = (-21)
abs(-21) = 21

and

2^2 + (5i)^2 = 4 + (-25)
abs(4) + abs(-25) = 29

The latter seems more physically sound to me, but the former seems more mathemathically sound. Can anyone clear this up for me?

2. Aug 18, 2010

### betel

The imaginary part is the part standing next to the "i", so in your example the 5 itself. Then you get the absolute value of the complex number by
$$|z|^2 = \Re(z)^2+\Im(z)^2$$
Or by using the complex conjugate
$$|z|^2 = z \cdot \bar z$$

For the first part I suspect you write your complex number in polar coordinates
$$z = r \exp{i \xi}$$
In this case the absolute value would be just $$|z|=r$$

3. Aug 18, 2010

### TubbaBlubba

Ah, I think I see, the absolute value is the distance from the origin? Thanks for clearing it up.

4. Aug 18, 2010

### betel

Yes. If you draw the complex number in the complex plane you can recognize the above formula as an application of Pythagoras' theorem.