Finding real part of an expression.

[MathematicalPhysicist]

Hi, I have the next expression:

$$\frac{iw+3}{(iw-3)(iw+6)(iw+1)}$$

Now I want to find the real part of this expression via mathematica or maple, and for the love of god it doesn't work, what have I done wrong here?!

the codes and their errors are in the attachments.
http://oi50.tinypic.com/25zs684.jpg
http://oi50.tinypic.com/24wfqt3.jpg

Peace out!

N.B
w is real parameter.

 

[Bill Simpson]

In[1]:= FullSimplify[Reduce[a+I b==(I w+3)/((I w-3)(I w+6)(I w+1))&& a∈Reals&& b∈Reals&& w∈Reals,{a,b},Backsubstitution->True]]

Out[1]= w∈Reals &&
a == -((54 + 27*w^2 + w^4)/(324 + 369*w^2 + 46*w^4 + w^6)) &&
b == -((w*(-27 + w^2))/(324 + 369*w^2 + 46*w^4 + w^6))

Check this result very carefully before you depend on it

 

[MathematicalPhysicist]

Thanks. Who knew that such a simple task should have a long line of code?!

 

[Hepth]

What about "ComplexExpand"? ((Mathematica))

ComplexExpand[(I w + 3)/((I w - 3) (I w + 6) (I w + 1))]

$$-\frac{27 w^2}{\left(w^2+1\right) \left(w^2+9\right) \left(w^2+36\right)}-\frac{54}{\left(w^2+1\right) \left(w^2+9\right) \left(w^2+36\right)}-\frac{w^4}{\left(w^2+1\right) \left(w^2+9\right) \left(w^2+36\right)}\\+i \left(\frac{27 w}{\left(w^2+1\right) \left(w^2+9\right) \left(w^2+36\right)}-\frac{w^3}{\left(w^2+1\right) \left(w^2+9\right) \left(w^2+36\right)}\right)$$