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 ψ_{r}(x) and an imaginary part ψ_{i}(x), with the ψ’s being real valued functions, so Ψ(x) = ψ_{r}(x) +*i**ψ_{i}(x)), then multiplying Ψ(x) by its complex conjugate (Ψ^{*}(x) = ψ_{r}(x) – *i**ψ_{i}(x) , where *i* =√(-1) ) yields:

(ψ_{r}(x) + *i**ψ_{i}(x)) * (ψ_{r}(x) – *i**ψ_{i}(x))

which (using basic algebra’s FOIL method)

ψ_{r}^{2}(x) + ψ_{i}^{2}(x)

Which is real valued, as the ψ’s are real valued.

This is the basis for the ‘joke’. And its funny … really …