RE: Easy way to simplify expr to a+bi?

*To*: mathgroup at smc.vnet.net*Subject*: [mg26282] RE: [mg26245] Easy way to simplify expr to a+bi?*From*: "David Park" <djmp at earthlink.net>*Date*: Sun, 10 Dec 2000 00:19:54 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Christopher, Here is one method. Z = 1/(1/R1 + 1/(R2 + I*w*L) + I*w*C); Simplify[ComplexExpand[Re[Z], TargetFunctions -> {Re, Im}]] (R1*(R1*R2 + R2^2 + L^2*w^2))/(2*R1*R2 + R2^2 + L^2*w^2 + R1^2*(1 - 2*C*L*w^2 + C^2*w^2*(R2^2 + L^2*w^2))) Simplify[ComplexExpand[Im[Z], TargetFunctions -> {Re, Im}]] (R1^2*w*(L - C*R2^2 - C*L^2*w^2))/(2*R1*R2 + R2^2 + L^2*w^2 + R1^2*(1 - 2*C*L*w^2 + C^2*w^2*(R2^2 + L^2*w^2))) I have to admit that manipulating complex functions in Mathematica is not totally intuitive! David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > From: crcarle at sandia.gov [mailto:crcarle at sandia.gov] To: mathgroup at smc.vnet.net > Hi: > > I often encounter complex expressions such as: > > Z = 1/( 1/R1 + 1/( R2 + I w L ) + I w C ) > > which I want to simplify to the form of > > Z = a + b I > > so I can answer various questions about the behavior of either a or b . > > I can do this by hand of course, tediously adding the fractions, > inverting, multiplying by the complex conjugate on top and bottom, then > simplifying a long list of terms until I get there. > > It would be nice if I could do the equivalent of Re[Z] and Im[Z] and > have Mathematica do the work for me, but that is not the result of those > functions. > > Any ideas? > > Thanks. > -- > _______________________ > Christopher R. Carlen > Sr. Laser/Optical Tech. > Sandia National Labs > >