Can Mathematica evaluate
Arg[1+ I a] when
a is a positive real in order to get
For example (this is much simpler than the code I'm working with):
ComplexExpand[Im[1/Sqrt[1 + I a]]]
-(Sin[1/2 Arg[1 + I a]]/(1 + a^2)^(1/4)).
This is a calculation in the middle of my code, and I'm too lazy to replace
Arg[1+ i a] for
ArcTan[a] manually every time the code is run. Moreover, in the following lines of that code I would like to have only real variables in order to use the function
Simplify instead of
ComplexExpand, otherwise I get
-(1/2) Arg[1 - (I a)/b] + 1/2 Arg[1 + (I a)/b].
Simplify[-(Sin[1/2 Arg[1 + I a]]/(1 + a^2)^(1/4)), a ∈ Reals]
doesn't do anything.