From xkcd Heh … If you don’t know what a complex conjugate is, read this. Basically, if I have a function Ψ(x) which has a “real” part Ïr(x) and an imaginary part Ïi(x), with the Ï’s being real valued functions, so Ψ(x) = Ïr(x) +i**Ïi(x)), then multiplying Ψ(x) by its complex conjugate (Ψ(x) = Ïr(x) - *i**Ïi(x) , where i =â(-1) ) yields:
(Ïr(x) + *iÏi(x)) * (Ïr(x) - *iÏi(x))
which (using basic algebra’s FOIL method) Ïr2(x) + Ïi2(x) Which is real valued, as the Ï’s are real valued. This is the basis for the ‘joke’. And its funny … really …