I will start with the following example. If say I want to calculate the abs value of a complex numeber for instance: Abs[a+i*b].
The result is of course a^2+b^2, but mathematica leavs it unevaluated. I understand this is because it doesn't know whether the symbols a and b are complex themselves. I've seen in the help file a section about making assumptions with the simplify command. I've tried using Simplify[Abs[a+i*b,a Reals && b Reals] but the expression is still unevaluated.
In short how can tell Mathematica that a and b are Real? I've encounterd this problem in other functions as well.