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Re: Complex arithmetic identity question

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this sort of thing is one of the most frustrating issues many 
Mathematica novices face. The difficulty is that, by default, 
Mathematica considers that symbolic quantities such as your a and b, may 
be complex, whereas you presumably think of them as being real in this 
context. Then you have to tell it your intention by using ComplexExpand.

In the outputs below, I'm showing the Input form of results, so they are 
1-dimensional rather than built-up in 2 dimensions.

   ComplexExpand[1/(a + I b)]
a/(a^2 + b^2) - (I*b)/(a^2 + b^2)

Now if you really want to assign the (assumed) real and imaginary parts 
of that result to c and d in a complex number c + d I, you could do it 
like this:

   ComplexExpand[Through[{Re, Im}[1/(a + I b)]]]
{a/(a^2 + b^2), -(b/(a^2 + b^2))}

On 5/13/2011 6:24 AM, Ralph Dratman wrote:
> c + I d = 1/(a +I b)

-- 
Murray Eisenberg                     murray@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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Re: Complex arithmetic identity question Murray Eisenberg <murray@math.umass.edu> - 2011-05-14 07:11 +0000

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