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Re: DirectedInfinity[1 + I], why does it get replaced by (1 + I)/(sqrt(2) ?
On 6 Apr 2005, at 09:11, 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:= DirectedInfinity[1 + I] DirectedInfinity[I] > Out:= 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:= DirectedInfinity[1 + I] > Out:= 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 > Because (1 + I)/Sqrt is a complex number of modulus 1, or a "unit vector", and unit vectors are normally used to indicate direction (there is a unique unit vector in a given direction). Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/andrzej/index.html http://www.mimuw.edu.pl/~akoz/