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Sorry, this trivial eg is still way over my head. Is it related to (high school) polnomials always having complex roots, but not necessarily real roots? But th
by hyperpallium2 5y ago
Sorry, this trivial eg is still way over my head.
Is it related to (high school) polnomials always having complex roots, but not necessarily real roots? But that constraint on reals seems like "structure" to me, and complex numbers lack this structure...?
(It may well just require a few more years math on ny part.)
- btilly 5y agoYes. Polynomials over the complex numbers can always be factored completely based on the roots. Polynomials over the real numbers cannot. The result is easy to prove using complex analysis, which uses the 2-D structure of the complex numbers to prove it.