Re: How to get the Real and Imaginary part of an expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg129340] Re: How to get the Real and Imaginary part of an expression*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 5 Jan 2013 02:21:05 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20130103021627.CBD1368B0@smc.vnet.net>

Since there seems to be some typo or else some spurious control code ("=882") in the numerator of your fraction, for purposes of explanation I'll change the numerator just to w. In general, the way to extract the real and imaginary parts of a complex number is to use ComplexExpand along with, of course, Re and Im. Here, though, you have both real and complex variables, so I think you'll need to express the complex s in the form x + I y. Then applying ComplexExpand will treat all the variables w, z, x, and y as real: ComplexExpand[Re[(w)/(s^2 + 2*z*w*s + w^2) /. s -> x + I y]] w^3/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) + (w*x^2)/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) - (w*y^2)/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) + (2*w^2*x*z)/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) And similarly for Im. (I've shown the results in one-dimensional InputForm for purposes of this plain-text e-mail.) On Jan 2, 2013, at 9:16 PM, Eduardo M. A. M. Mendes <emammendes at gmail.com> wrote: > Hello > > I need to extract the real and imaginary part of the following expression > > (w=882)/(s^2+2*z*w*s+w^2) > > where w and z are positive constants. s is a complex variable. > > Applying Re and Im to the expression does not do much. By hand, one can easily find them. > > What am I missing? > > many thanks > > Ed > > --- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2838 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**How to get the Real and Imaginary part of an expression***From:*"Eduardo M. A. M. Mendes" <emammendes@gmail.com>