Re: Dividing complex numbers
- From: Bill Dubuque <wgd@xxxxxxxxxxxxxxxxxxxx>
- Date: 18 Nov 2007 16:05:39 -0500
magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
jehugaleahsa@xxxxxxxxx <jehugaleahsa@xxxxxxxxx> wrote:
You divide two complex numbers by taking the conjugate of the
denominator and multiplying the dividend and denominator by it.
Now, I assume this is valid because a complex number divided by itself
is equal to 1 + 0i.
How is it that we can say it is 1 + 0i? Is it an axiom?
Otherwise, I feel like we are solving division by using division.
Division is multiplication by the multiplicative inverse.
Probably the OP defines a/b to be the solution of b x = a
and wonders why he cannot find any axioms for this operation.
The trick of rationalizing denominators generalizes to compute
inverses in any algebraic extension of a field, since one can
read off the inverse of w from any polynomial that it satisfies,
i.e. 0 = f(w) = w g(w) - d -> 1/w = g(w)/d. More generally,
if D<E is an integral extension of domains, field D <-> field E
See also my prior posts [1],[2].
--Bill Dubuque
[1] http://google.com/groups?selm=y8zr7j536ec.fsf%40nestle.csail.mit.edu
[2] http://google.com/groups?selm=y8zwtid4b0u.fsf%40nestle.csail.mit.edu
.
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- Dividing complex numbers
- From: jehugaleahsa@xxxxxxxxx
- Re: Dividing complex numbers
- From: Arturo Magidin
- Dividing complex numbers
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