For a physics experiment, I have a signal that is a complex number. This signal has independent rotating phases in it. phase 1: a1 and phase 2: a2 I can write my signal as a complex number
F and B are complex c is real i=sqrt(-1)
What is the expected value of Abs(Z) and of its total phase Arg(Z) knowing that a1 and a2 are uniformly distributed on the interval [0 2pi]
Is there an analytical formula for and ? How to derive it?
I supposed it has to do with functions of random variables. I've looked in math books but I feel that I won't have the time come with the answer myself.