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Re: Complex arithmetic identity question

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Simplify[Solve[{c + I d == 1/(a + I b),
    Element[{a, b, c, d}, Reals]}, {c, d}], Element[{a, b}, Reals]]

{{c -> a/(a^2 + b^2), d -> -(b/(a^2 + b^2))}}

I don't think Simplify (assuming what was already assumed) should be  
needed... but it is.

Bobby

On Fri, 13 May 2011 05:24:25 -0500, Ralph Dratman  
<ralph.dratman@gmail.com> wrote:

> Hi. I am new to the mailing list, trying to learn how to persuade
> Mathematica to perform helpful algebraic manipulations.
>
> Here is a very very simple example. I think this should be easy, but so  
> far
> I have not been able to figure it out.
>
> Suppose  c + I d = 1/(a +I b), where a, b, c, d are reals. Solve for c  
> and d
> in terms of a and b.
>
> For a human, the solution is easy. Multiply top and bottom by the complex
> conjugate, then set real part equal to real part, imaginary part equal to
> imaginary part.
>
> The result is  c -> a/(a^2+b^2),  d -> -b/(a^2+b^2).  But is there a  
> simple
> way to get Mathematica to give me that answer in one step?
>
> If I help by solving for c by hand and plugging that in, Mathematica  
> knows
> how to finish the job:
>
>    In[22]:= Solve[1/(a + I b) == a/(a^2 + b^2) + I d, d]
>
> Out[22]= {{d -> -(b/(a^2 + b^2))}}
>
>
> But I was hoping Mathematica would be able to go all the way from the
> equation to the solution in one step, with the use of Solve or something
> similar.
>
>
> Is this possible, and if so, how? If not, why not?
>
>
> Thank you.
>
> Ralph Dratman


-- 
DrMajorBob@yahoo.com

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Re: Complex arithmetic identity question DrMajorBob <btreat1@austin.rr.com> - 2011-05-14 07:11 +0000

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