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Topic: How to get the Real and Imaginary part of an expression
Replies: 10   Last Post: Jan 5, 2013 2:18 AM

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Murray Eisenberg

Posts: 16
Registered: 4/14/10
Re: How to get the Real and Imaginary part of an expression
Posted: Jan 5, 2013 2:18 AM
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I forgot that ComplexExpand can take an optional 2nd argument specifying
any variables that should be treated as complex rather than as real.
Hence you can also do the following (again with results shown in
InputForm):

ComplexExpand[Re[(w)/(s^2 + 2*z*w*s + w^2)], s]
w^3/((2*w*z*Im[s] + 2*Im[s]*Re[s])^2 + (w^2 - Im[s]^2 + 2*w*z*Re[s] + Re[s]^2)^
2) - (w*Im[s]^2)/((2*w*z*Im[s] + 2*Im[s]*Re[s])^2 +
(w^2 - Im[s]^2 + 2*w*z*Re[s] + Re[s]^2)^2) +
(2*w^2*z*Re[s])/((2*w*z*Im[s] + 2*Im[s]*Re[s])^2 +
(w^2 - Im[s]^2 + 2*w*z*Re[s] + Re[s]^2)^2) +
(w*Re[s]^2)/((2*w*z*Im[s] + 2*Im[s]*Re[s])^2 +
(w^2 - Im[s]^2 + 2*w*z*Re[s] + Re[s]^2)^2)

Perhaps that better suits your purposes (although to my eye it's a lot
harder to read than my original version that replaces s by x + I y).


On Jan 3, 2013, at 9:17 AM, Murray Eisenberg <murray@math.umass.edu> wrote:

> Since there seems to be some typo or else some spurious control code
("=882") in the numerator of your fraction, for purposes of
explanation I'll change the numerator just to w.
>
> In general, the way to extract the real and imaginary parts of a

complex number is to use ComplexExpand along with, of course, Re and Im.
Here, though, you have both real and complex variables, so I think
you'll need to express the complex s in the form x + I y. Then applying
ComplexExpand will treat all the variables w, z, x, and y as real:
>
> ComplexExpand[Re[(w)/(s^2 + 2*z*w*s + w^2) /. s -> x + I y]]
> w^3/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) +
> (w*x^2)/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) -
> (w*y^2)/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2) +
> (2*w^2*x*z)/((w^2 + x^2 - y^2 + 2*w*x*z)^2 + (2*x*y + 2*w*y*z)^2)
>
> And similarly for Im.
>
> (I've shown the results in one-dimensional InputForm for purposes of

this plain-text e-mail.)
>
>
> On Jan 2, 2013, at 9:16 PM, Eduardo M. A. M. Mendes

<emammendes@gmail.com> wrote:
>
>> Hello
>>
>> I need to extract the real and imaginary part of the following

expression
>>
>> (w=882)/(s^2+2*z*w*s+w^2)
>>
>> where w and z are positive constants. s is a complex variable.
>>
>> Applying Re and Im to the expression does not do much. By hand, one

can easily find them.
>>
>> What am I missing?


---
Murray Eisenberg murrayeisenberg@gmail.com
80 Fearing Street phone 413 549-1020 (H)
Amherst, MA 01002-1912








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