I'm sorry if this question is too metaphysical, but I will give it a try.
My textbook in introductory quantum mechanics is basing a lot of its proof and derivations on the fact that the value of the measurement must be a real value, hence no imaginary part. This is stated as something obvious and in a way taken as an axiom.
Is there any example of a measurement that is in fact a complex or imaginary number, and even if there is not, is it a bit naive to state that there can't be complex measurements? We may indeed measure non-rational values, negative values even though these numbers were not always considered numbers.
