Re: Complex arithmetic identity question
- To: mathgroup at smc.vnet.net
- Subject: [mg118878] Re: Complex arithmetic identity question
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Sat, 14 May 2011 03:06:44 -0400 (EDT)
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 at math.umass.edu
Mathematics & Statistics Dept.
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University of Massachusetts 413 545-2859 (W)
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