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phil ess

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**[RESOLVED] Quick complex numbers question in QM (probability amplitues)**

Im a little confused here. I am reading in my textbook about probability amplitudes in Stern Gerlach measurements, and it says this:

We find the resulting probabilities for deflection of [tex]\left(\stackrel{\alpha}{\beta}\right)[/tex] in the x and y directions as:

[tex]Prob(\pm in x) = \left|\frac{\alpha\pm\beta}{\sqrt{2}}\right|^2 = \frac{1}{2}(|\alpha|^2 + |\beta|^2 \pm \alpha*\beta \pm \beta*\alpha) = \frac{1}{2} \pm Re(\alpha*\beta)[/tex]

[tex]Prob(\pm in y) = \left|\frac{\alpha\mp i\beta}{\sqrt{2}}\right|^2 = \frac{1}{2}(|\alpha|^2 + |\beta|^2 \mp i\alpha*\beta \mp i\beta*\alpha) = \frac{1}{2} \pm Im(\alpha*\beta)[/tex]

Now I understand where the amplitudes come from and everything, the thing I don't understand is the functions Re and Im, and how they simplified the amplitudes to

[tex]\frac{1}{2} \pm Re(\alpha*\beta)[/tex]

and

[tex]\frac{1}{2} \pm Im(\alpha*\beta)[/tex]

So can someone please explain these functions Re and I am and how they work here?

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