What is the expected value for two complex numbers with known modulus and uniformly distributed phase?

Question

It seems easy to prove that for $a=|a|e^{-j\arg(a)}$ and $b=|b|e^{-j\arg(b)}$, the expected value for the squared sum is $E\left[(a+b)^2\right]=|a|^2+|b|^2$. On the other side, the expected value $E\left[|a+b|\right]$ seems to be more tricky. Is there any reference for this quantity?