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I've to do some complex calculation with Mathematica and if I put in my code it gives me something big back, so is it possible to say that my variables are strictly real numbers, by sing the FullSimplify option?

My code:

FullSimplify[Abs[(230)*((230)/(((((r)*(I*100*Pi*l))/((r)+(I*100*Pi*l)))*((s+t+(I*100*Pi*m)+(I*100*Pi*n))))/((((r)*(I*100*Pi*l))/((r)+(I*100*Pi*l)))+((s+t+(I*100*Pi*m)+(I*100*Pi*n))))))]]

And all my variables are real and bigger than zero (r,s,l,t,m,n)! How can I that fit in in my code to make the outcome more likeable, an option that makes my code as small as possible?

Thanks in advance

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5
  • $\begingroup$ FullSimplify would be a start and reset variable/define variable $\endgroup$
    – user9660
    Sep 27, 2015 at 8:37
  • $\begingroup$ I've edited my last part, thanks for your comment $\endgroup$ Sep 27, 2015 at 8:48
  • $\begingroup$ Fullsimplify is not FullSimplify $\endgroup$
    – user9660
    Sep 27, 2015 at 8:49
  • $\begingroup$ Oh I didn't know that $\endgroup$ Sep 27, 2015 at 9:14
  • 1
    $\begingroup$ ComplexExpand. 15char $\endgroup$
    – LLlAMnYP
    Sep 27, 2015 at 12:32

1 Answer 1

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By reading the documentation you see that FullSimplify allows Assumptions, similar to Assuming which could also help using ComplexExpand

FullSimplify[
 ComplexExpand[
  Abs[(230)*((230)/(((((r)*(I*100*Pi*l))/((r) + (I*100*Pi*l)))*((s + 
             t + (I*100*Pi*m) + (I*100*Pi*
               n))))/((((r)*(I*100*Pi*l))/((r) + (I*100*Pi*
                l))) + ((s + t + (I*100*Pi*m) + (I*100*Pi*n))))))]]
 , Assumptions -> And @@ Thread[Greater[{r, s, t, m, n, l}, 0]]]

Mathematica graphics

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