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Re: Forcing Re[]'s to be Real
*To*: mathgroup at smc.vnet.net
*Subject*: [mg18237] Re: [mg18223] Forcing Re[]'s to be Real
*From*: Daniel Lichtblau <danl at wolfram.com>
*Date*: Thu, 24 Jun 1999 14:24:19 -0400
*References*: <199906230041.UAA04398@smc.vnet.net.>
*Sender*: owner-wri-mathgroup at wolfram.com
Anthony Foglia wrote:
>
> I seem to have found an interesting problem involving computing the
> real part of complex numbers. (Interesting, in that it wasn't there a few
> weeks ago when I ran the (as-far-as-i-can-remember) exact same code.)
>
> I have a complex function:
>
> k[w] := Sqrt[w^2 (1 + (2 / (1 + I w)))]
>
> I want to graph the real and imaginary parts, but Mathematica doesn't want
> to express the Re[k[w]] as a real number. What do I mean? Well, if I
> type:
>
> Re[Sqrt[1+I]]
>
> I get out
>
> Re[Sqrt[1+I]]
>
> Same if I do Re[ComplexExpand[Sqrt[1+I]]], or Re[(1+I)^(1/2)]. But if I
> enter:
>
> Re[ComplexExpand[(1+I)^(1/2)]
>
> Mathematica is kind enough to respond with:
>
> 2^(1/4) Cos[Pi/8]
>
> I'm certain that this is the root of my problem, but I'll be damned if I
> know why Mathematica doesn't like it now, but did a few weeks ago. Any
> help?
>
> --Anthony
I could not replicate your findings in any current version of
Mathematica (that is, version 3 or 4), although I got something along
the lines of what you say using version 2.2. The way to get the sort of
result you want (this is true in general, independent of version) is to
reverse the order of ComplexExpand and Re. In version 2.2:
In[2]:= ComplexExpand[Re[Sqrt[1+I]]]
1/4 Pi
Out[2]= 2 Cos[--]
8
Daniel Lichtblau
Wolfram Research
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