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Re: complex analysis problem in mathematica 3.0


Hs[s_] = 1/(s^3+2s^2+2s+1);

Hs[I*w]

1/((-I)*w^3 - 2*w^2 + 2*I*w + 1)

ComplexExpand[%]

-((2*w^2)/((1 - 2*w^2)^2 + (2*w - w^3)^2)) + 
  I*(w^3/((1 - 2*w^2)^2 + (2*w - w^3)^2) - 
    (2*w)/((1 - 2*w^2)^2 + (2*w - w^3)^2)) + 
  1/((1 - 2*w^2)^2 + (2*w - w^3)^2)

Collecting the Real terms

FullSimplify[%, ExcludedForms->I*_]

(1 - 2*w^2)/(w^6 + 1) + 
  I*(w^3/((1 - 2*w^2)^2 + (2*w - w^3)^2) - 
    (2*w)/((1 - 2*w^2)^2 + (2*w - w^3)^2))

Collecting the imaginary terms

Together /@ %

(1 - 2*w^2)/(w^6 + 1) + (I*(w^3 - 2*w))/(w^6 + 1)

This can all be done in one step

Hw[w_] = Together /@ FullSimplify[ComplexExpand[Hs[I*w]], ExcludedForms-
>I*_];

Verifying

Hs[I*w] == Hw[w] // Simplify

True

> 
> From: BranasMan <branasREmoVe at mail.inet.hr>
To: mathgroup at smc.vnet.net
> Date: 2004/05/31 Mon AM 12:13:36 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg48473] [mg48459] complex analysis problem in mathematica 3.0
> 
> i have a complex function:
> 
> H(s)=1 / (s^3 + 2s^2 + 2s + 1)
> 
> whan i replace "s" with j*w (j=sqrt(-1)) i get:
> 
> H=1 / (1 + j2w -2w^2 - jw^3)
> 
> i would like to get that function in shape of : 
> H=something + j*something_else i.e. the complex
> and real part apart.
> 
> i played with Re and Im,but it seems that the fact that
> "w" is a variable confuses mathematica?!
> 
> i would reeeealy appreciate any help,and maybe perhaps some
> links for me to learn to use mathematica better.
> 

Bob Hanlon
Chantilly, VA


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