How should I interpret the difference between f^2(t) and |f(t)|^2? I don't see how they are different, but an application that I'm studying indicates that they are uniquely different. Don't both notatations indicate a squaring of the function?
If f is a real valued function then there is no difference between and . For real numbers, absolute value can be defined as so that .
If f is complex valued, there is a difference: If f(x)= ix, then , while .