Re: complex analysis problem in mathematica 3.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg48473] Re: [mg48459] complex analysis problem in mathematica 3.0*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 1 Jun 2004 03:02:49 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

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