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))]

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

 

[alphy]

I understand your frustration with trying to find the real part of this expression using Mathematica or Maple. However, it seems that there may be some errors in the codes that you have provided. For example, in the first attachment, it appears that you have used the variable "x" instead of "w" in the expression. Also, in the second attachment, you have not defined the variable "w" before using it in the expression.

One possible solution could be to use the "Re" function in Mathematica or Maple, which calculates the real part of a complex number or expression. For example, in Mathematica, you could write:

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

This should give you the real part of the expression. However, please make sure to define the variable "w" before using it in the expression.

I hope this helps and good luck with your research!