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Oder vielleicht besser (?) :
In[1]:= f[z_]:=
(ComplexExpand[Re[z],TargetFunctions->{Re,Im}] +
I ComplexExpand[Im[z],TargetFunctions->{Re,Im}])/.
{Re[r_]:>r,Im[i_]:>0}
In[2]:= f[Abs[a+I*b]]
2 2
Out[2]= Sqrt[a + b ]
In[3]:= f[ (a + I b)/(a^2 - I b) ]
3 2 2
a b a b a b
Out[3]= ------- - ------- + I (------- + -------)
4 2 4 2 4 2 4 2
a + b a + b a + b a + b
Rolf
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