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Re: Forcing Re[]'s to be Real
*To*: mathgroup at smc.vnet.net
*Subject*: [mg18239] Re: Forcing Re[]'s to be Real
*From*: "David Keith" <dkeith at sarif.com>
*Date*: Thu, 24 Jun 1999 14:24:20 -0400
*Organization*: Hevanet Communications
*References*: <7kpbj1$4b8@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Anthony,
Two things I think:
1) Your definition assigned to k[w] instead of k[w_],
2) Re[] doesn't seem to want to approximate the exact number Sqrt[Complex],
but Re[Complex]//N ans Re[ApproximateComplex] works fine. Since plot uses
N[] it seems to work fine also.
Dave
See below:
In[295]:=
k[w_] := Sqrt[w^2 (1 + (2 / (1 + I w)))]
In[305]:=
Re[k[1]]
Out[305]=
\!\(Re[\ at \(2 - \[ImaginaryI]\)]\)
In[306]:=
Re[k[1.]]
Out[306]=
1.45535
In[298]:=
Re[k[1]] // N
Out[298]=
1.45535
In[299]:=
Im[k[1]] // N
Out[299]=
-0.343561
Plot[{Re[k[x]], Im[k[x]]}, {x, -5, 5}]
Anthony Foglia wrote in message <7kpbj1$4b8 at smc.vnet.net>...
> 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
>
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