Did you try a search in the Documentation Center? If you do, one of the things you'll find near the top of the hits is
Complex Numbers (Mathematica Guide)
which includes a list of functions. One of these is:
ComplexExpand - expand symbolic expressions into real and imaginary parts
Then look at the reference page for that; it's what you want here.
ComplexExpand[Re[1/(x + y I)]] x/(x^2 + y^2)
The Refine and the assumptions about x and y are superfluous: the whole point of ComplexExpand is that it assumes symbolic variables used within it are already real.
On Feb 26, 2013, at 1:09 AM, Brentt <email@example.com> wrote:
> > Hello, > > I was wondering why this works > > IN:= Refine[Re[x + y I], Element[x , Reals] && Element[y , Reals]] > > Out:= x > > But this does not > > In:= Refine[Re[1/(x + y I)], Element[x , Reals] && Element[y , Reals]] > > Out:= Re[1/(x + y I)] > > > > Is there a nice built in way to get the real and imaginary parts of a > complex function? >
--- Murray Eisenberg firstname.lastname@example.org 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