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Re: Forcing Re[]'s to be Real
*To*: mathgroup at smc.vnet.net
*Subject*: [mg18281] Re: Forcing Re[]'s to be Real
*From*: pitakc at ee.pdx.edu (Pitak Chenkosol)
*Date*: Fri, 25 Jun 1999 15:05:25 -0400
*References*: <7kpbj1$4b8@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hello,
How about the followings : (I cut and paste from a DOS window so the format
may not look good but you get the idea)
In[1]:= k[w_] := Sqrt[w^2 (1 + (2/(1 + I w)))]
In[2]:= ComplexExpand[Re[k[w]]]
2
Arg[1 + -------]
2 2 1 + I w
Out[2]= Sqrt[w ] Sqrt[Abs[1 + -------]] Cos[----------------]
1 + I w 2
In[3]:= ComplexExpand[Im[k[w]]]
2
Arg[1 + -------]
2 2 1 + I w
Out[3]= Sqrt[w ] Sqrt[Abs[1 + -------]] Sin[----------------]
1 + I w 2
In[4]:= ComplexExpand[Re[k[11/17]]]
187
ArcTan[---]
1361 1/4 494
11 (----) Cos[-----------]
205 2
Out[4]= -----------------------------
17
In[5]:= ComplexExpand[Im[k[11/17]]]
187
ArcTan[---]
1361 1/4 494
-11 (----) Sin[-----------]
205 2
Out[5]= ------------------------------
17
In[6]:= ComplexExpand[Re[k[11/17]]]//N
Out[6]= 1.0217
In[7]:= ComplexExpand[Im[k[11/17]]]//N
Out[7]= -0.186906
Hope that help.
Regards,
Pitak
-----
afoglia at hal.physics.ucsb.edu (Anthony Foglia) writes:
> 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
--
Pitak Chenkosol, Dept. Electrical Eng.,| " I was born not knowing and have
Portland State University, | only had a little time to change
P.O. Box 751, Portland, OR 97207-0751. | that here and there."
E-mail: pitakc at ee.pdx.edu | Richard P. Feynman
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