Hi all,

I am pretty new in Mathematica, so that might be a simple question!

I am defining a function in complex space, then I am trying to use its module and argument (Abs and arg). At the end of the day, I'd like to take derivative of that. The output seems pretty weird for me. I am getting Abs' and do not know how to deal with that. Here is the sample of my work:

T1[A_, B_, f] = (A + I*B)*f;
Rho1 = Log[Abs[T1[A, B, f]]] - Log[Abs[11 + I*22]]
D[Rho1, A]
(f Abs'[(A + I B) f])/Abs[(A + I B) f]

And even when I evaluate that after ComplexExpand at a simple point it gives me wrong answer:

ComplexExpand(f Abs'[(A + I B) f])/
 Abs[(A + I B) f] /. {A -> 2 , B -> 1 , f -> 100}
1/Sqrt[5]

But it should be 2/5!

I am wondering if any one has some idea in relate of that. I have attached the file as well.

Thanks, Sardar

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