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


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


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