Real Number Expectation Value: Explanation & QM Example

[dyn]

hi. I have been looking at a QM example in a book. It works out the expectation value for momentum which I know should be a real number but I can't see how or why the following number is real
α and β are complex numbers with | α |² + | β |² = 1 and ω and t are real

-i ( α^*β e^-iωt -αβ^*e^iωt)

Can anyone tell me if this is a real number and why?
Thanks

 

[mfb]

The two parts in the bracket are the complex conjugates of each other: They have the same real component but opposite imaginary component. Their difference has a real component of zero, it is purely imaginary. If you multiply that by -i you get a real number.

 

[dyn]

Thanks. I just couldn't see it but now I can. Thanks again