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- expression. Roots are used for determining the radius of convergence of a power series with the root test. The nth roots of 1 are called roots of unity and play…32 KB (4.773 Wörter) - 20:22, 4. Apr. 2025
- Gaussian period (Kategorie All articles with unsourced statements)mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of roots of unity. The periods permit explicit calculations in cyclotomic fields…7 KB (1.130 Wörter) - 05:22, 28. Mär. 2021
- Cubic equation (Weiterleitung von „Factorization of cubic functions“)the same field as the coefficients. For example, some cubic equations with rational coefficients have roots that are irrational (and even non-real) complex…68 KB (10.311 Wörter) - 10:24, 26. Mai 2025
- Dirichlet's unit theorem (Weiterleitung von „Regulator of an algebraic number field“)in practice the calculations are quite involved when n is large. The torsion in the group of units is the set of all roots of unity of K, which form a…13 KB (1.756 Wörter) - 16:22, 15. Feb. 2025
- Slide rule (Kategorie Pages displaying short descriptions of redirect targets via Module:Annotated link)scale displaying the logarithm of the logarithm. This allowed the user to directly perform calculations involving roots and exponents. This was especially…67 KB (8.395 Wörter) - 04:53, 23. Jun. 2025
- Factorization (Weiterleitung von „Sum and difference of powers“)that appear in the nth row of Pascal's triangle. The nth roots of unity are the complex numbers each of which is a root of the polynomial x n − 1. {\displaystyle…42 KB (7.863 Wörter) - 15:39, 5. Jun. 2025
- Hensel's lemma (Kategorie Articles with short description)\mathbb {Z} _{p}} cannot contain the root of unity μ p {\displaystyle \mu _{p}} . Although the pth roots of unity are not contained in F p {\displaystyle…42 KB (9.044 Wörter) - 22:58, 24. Mai 2025
- Complex number (Weiterleitung von „Classification of complex numbers“)vice versa. With algebraic methods, more specifically applying the machinery of field theory to the number field containing roots of unity, it can be shown…91 KB (12.021 Wörter) - 19:33, 29. Mai 2025
- Quadratic equation (Kategorie Articles with short description)For example, let a denote a multiplicative generator of the group of units of F4, the Galois field of order four (thus a and a + 1 are roots of x2 +…53 KB (6.663 Wörter) - 22:04, 15. Apr. 2025
- Number (Weiterleitung von „History of numbers“)root of x3 − 1 = 0 (now called Eisenstein integers). Other such classes (called cyclotomic fields) of complex numbers derive from the roots of unity xk…67 KB (8.504 Wörter) - 18:14, 25. Jun. 2025
- Square root (Weiterleitung von „List of square roots“)by itself, or y ⋅ y {\displaystyle y\cdot y} ) is x. For example, 4 and −4 are square roots of 16 because 4 2 = ( − 4 ) 2 = 16 {\displaystyle 4^{2}=(-4)^{2}=16}…48 KB (6.213 Wörter) - 23:46, 11. Jun. 2025
- Imaginary unit (Weiterleitung von „Square root of minus one“)associated with k = 0 is the principal n-th root of i. The set of roots equals the corresponding set of roots of unity rotated by the principal n-th root of i…30 KB (4.171 Wörter) - 11:38, 24. Jun. 2025
- Mirifici Logarithmorum Canonis Descriptio (Weiterleitung von „Description of the Wonderful Canon of Logarithms“)notation works with some examples. He also introduces a form of interval arithmetic to bound any errors that occur in his calculations.: p.8 : Sec.3ff : p…26 KB (3.373 Wörter) - 04:22, 16. Mai 2025
- Quadratic field (Kategorie Articles with short description)obtained as a subfield of a cyclotomic field of D {\displaystyle D} -th roots of unity. This expresses the fact that the conductor of a quadratic field is…12 KB (1.306 Wörter) - 04:09, 26. Jun. 2025
- Exponentiation (Weiterleitung von „Raised to the power of“)The nth roots of unity allow expressing all nth roots of a complex number z as the n products of a given nth roots of z with a nth root of unity. Geometrically…107 KB (13.693 Wörter) - 13:55, 23. Jun. 2025
- Thermodynamic activity (Kategorie Dimensionless numbers of chemistry)phase equilibrium calculations UNIQUAC model – phase equilibrium calculations Lewis, Gilbert Newton (1907). "Outlines of a new system of thermodynamic chemistry"…22 KB (3.015 Wörter) - 05:34, 26. Mai 2025
- Splitting field (Weiterleitung von „Construction of splitting fields“)two distinct roots of p will contain the quotient between two distinct cube roots of unity. Such a quotient is a primitive cube root of unity—either ω 2…17 KB (2.875 Wörter) - 06:25, 19. Mai 2025
- Étale cohomology (Kategorie Topological methods of algebraic geometry)H i(X, Gm) vanish if i ≥ 2. If μn is the sheaf of n-th roots of unity and n and the characteristic of the field k are coprime integers, then: H i ( X…33 KB (5.016 Wörter) - 01:02, 26. Mai 2025
- Unit (ring theory) (Weiterleitung von „Group of units“){\displaystyle \mu _{R}} is the (finite, cyclic) group of roots of unity in R and n, the rank of the unit group, is n = r 1 + r 2 − 1 , {\displaystyle…11 KB (1.526 Wörter) - 00:40, 6. Mär. 2025
- Imaginary number (Weiterleitung von „Square roots of negative numbers“)used when working with imaginary numbers that are expressed as the principal values of the square roots of negative numbers. For example, if x and y are…12 KB (1.347 Wörter) - 04:23, 8. Mai 2025
- Cube root (Weiterleitung von „Cube roots“)numbers. Otherwise, the three cube roots are all nonreal. For example, the real cube root of 8 is 2 and the other cube roots of 8 are − 1 + i 3 {\displaystyle…15 KB (2.266 Wörter) - 18:35, 21. Mai 2025
- country free of ethnic discrimination, and is often fixated on a period in the past when there was great unity between the Third World countries of Asia, Africa
- Göttingen H. Davenport; A. Schinzel: Diophantine Approximation and Sums of Roots of Unity, S. 118 GDZ Göttingen J. Moser: Convergent Series Expansions for Quasi-Periodic