Re: DirectedInfinity[1 + I], why does it get replaced by (1 + I)/(sqrt(2) ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg55818] Re: [mg55802] DirectedInfinity[1 + I], why does it get replaced by (1 + I)/(sqrt(2) ?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 7 Apr 2005 05:09:56 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200504060711.DAA13652@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

Evidently, the resulting complex number inside the DirectedInfinity expression has complex modulus 1, so that number is suitable to represent a "pure direction", without a magnitude. If you think of a complex number as a vector in the real plane, then you're getting a unit vector with the same direction as the original vector. Of course it would have been nice to have this properly documented! Matt wrote: > Hello, > This isn't particularly important probably, however, I am trying to > learn as much about Mathematica as possible, and I thought this might > shed some light on a 'Why Mathematica does this or that' principle. > > I'm working my way through 'The Mathematica Guidebook for > Programming' and on page 177, he gives an example as follows: > > In[39]:= DirectedInfinity[1 + I] DirectedInfinity[I] > Out[39]:= DirectedInfinity[-(1 - I)/sqrt(2)] > > That puzzled me a bit, so I decided to see what Mathematica would do > with just the first part: > > In[40]:= DirectedInfinity[1 + I] > Out[40]:= DirectedInfinity[(1 + I)/sqrt(2)] > > I realize that (1 + I)/sqrt(2) is in the same direction as (1 + I), but > why did Mathematica change it to the more 'strange' form? > > Thanks, > > Matt > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**DirectedInfinity[1 + I], why does it get replaced by (1 + I)/(sqrt(2) ?***From:*"Matt" <anonmous69@netscape.net>