Timeline for Can an algebraic number on the unit circle have a conjugate with absolute value different from 1?
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Sep 14, 2010 at 19:40 | comment | added | Noah Stein | Thanks -- I forgot to turn my brain on. Now the argument makes much more sense. | |
| Sep 14, 2010 at 19:29 | comment | added | Andreas Blass | @Noah: The minimal polynomial of the (nontrivial) cube roots of unity is the quadratic $x^2+x+1$ and does not have 1 as a root. More generally, the only number whose minimal polynomial has 1 as a root is 1. | |
| Sep 14, 2010 at 18:25 | comment | added | Noah Stein | I'm a little confused: several times you use the "fact" that 1 is not a root of f, but plenty of other algebraic numbers on the unit circle have 1 as a root of their minimal polynomial, like the cube roots of unity. These have odd degree and the coefficients have non-symmetric minimal polynomial. Did you want some other assumptions on the algebraic number under consideration? | |
| Sep 14, 2010 at 13:46 | history | edited | KConrad | CC BY-SA 2.5 |
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| Sep 14, 2010 at 13:37 | history | edited | KConrad | CC BY-SA 2.5 |
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| Sep 14, 2010 at 13:32 | history | answered | KConrad | CC BY-SA 2.5 |