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Discussion of "ka'o zei namcu"
[parent] [root]
Comment #1: Parts
Curtis W Franks (Fri Mar 31 20:32:01 2017)

Should we mention what the properties of the complex number are? For
example, I am especially meaning things like the real part and imaginary
part of the number.

If x1 is filled explicitly, these could all be understood. Moreover, this
word can be used for the entire structure of C, so it would not be
especially helpful to talk about any particular number's properties. Doing
so would also not generalize from how real numbers are handled (well, they
could be handled in such a way - but there is some structure which is
atomic and all of its parts are just itself). Additionally, why should we
culturally prioritize the Cartesian decomposition over other decompositions
(such as radius-angle decomposition)?

On the other hand, it could be useful in some circumstances (such as when
talking about all complex numbers with real part 1/2, or when x1 is not
explicit).

Comment #2: Re: Parts
Curtis W Franks (Fri Mar 31 20:34:19 2017)

> Additionally, why should we
> culturally prioritize the Cartesian decomposition over other
decompositions
> (such as radius-angle decomposition)?

One reason: we are using "ka'o" which does this. If we wanted a different
decomposition, we could use something else (such as "ka'o'ei").

___

It should be noted, though, that there are other ways to express imaginary
numbers than just these two. For example, there is a certain structure on a
certain set of matrices which is isomorphic with C.

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