Every abelian extension of the rational numbers is contained in an extension of the rationals with one of these values, according to the Kronecker-Weber theorem.
Every abelian extension of the rational numbers is contained in an extension of the rationals with one of these values, according to the Kronecker-Weber theorem. A Gaussian period, an early predecessor of Galois theory, is defined as the sum of these values. Kummer extensions adjoin one of these values to a field which already contains at least one of them.These values are called "twiddle factors" when applied in the Cooley-Tukey algorithm. Liouville disproved LamÃ©'s proof of Fermat's Last Theorem by showing that a polynomial decomposition representing these values was non-unique. The eigenvectors of a circulant matrix must consist entirely of these numbers, which are the solutions to cyclotomic polynomials. The nth order of these values form a regular n-gon inscribed in the unit circle on the complex plane. They can be calculated using de Moivre's theorem. For 10 points, name these values which satisfy the equation "z to the n minus one equals zero."
Every abelian extension of the rational numbers is contained in an extension of the rationals with one of these values, according to the Kronecker-Weber theorem.
roots of unity [or De Moivre numbers before de Moivre is mentioned]