This is just to illustrate, in code, Gianlucas and Murrays earlier replies:
In[1]:= r[w_] := 200/(I w (10 I w + 1)) In[2]:= t = r[q] Out[2]= -((200 I)/((1 + 10 I q) q)) In[3]:= ComplexExpand@Re@t Out[3]= -(2000/(1 + 100 q^2))
You answered yourself: ComplexExpand is made precisely for that purpose:
ComplexExpand
ComplexExpand[ReIm[r[w]]]
I don't know why Simplify does not do the job automatically in your example.
Simplify
