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- are the nth roots of unity. Thus, since they are all just multiplied by the same scalar η, the sum of the nth roots equals zero. For example, the four different…57 KB (7.020 Wörter) - 21:41, 8. Dez. 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) - 04:22, 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…69 KB (10.364 Wörter) - 09:53, 11. Dez. 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 (8.364 Wörter) - 21:51, 17. Dez. 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 (1.783 Wörter) - 23:37, 9. Nov. 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}…49 KB (6.209 Wörter) - 16:39, 18. Dez. 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 (7.917 Wörter) - 10:31, 7. Nov. 2025
- 0 (Weiterleitung von „History of zero“)representing it with the lowercase Greek letter ό (όμικρον: omicron). However, after using the Babylonian placeholder zero for astronomical calculations they would…75 KB (8.188 Wörter) - 11:25, 3. Dez. 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 (12.023 Wörter) - 21:20, 11. Dez. 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. Another now familiar…26 KB (3.287 Wörter) - 14:04, 17. Nov. 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 (9.043 Wörter) - 10:43, 4. Dez. 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…29 KB (4.142 Wörter) - 23:43, 8. Dez. 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 (2.879 Wörter) - 15:37, 29. 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 (13.645 Wörter) - 04:30, 7. Dez. 2025
- Sexagesimal (Kategorie Articles with short description)Scientific American, Roots of Unity Barton, George A. (1908), "On the Babylonian origin of Plato's nuptial number", Journal of the American Oriental…27 KB (3.032 Wörter) - 09:06, 16. Dez. 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) - 15:54, 12. Sep. 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) - 14:21, 11. Dez. 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…106 KB (11.535 Wörter) - 00:34, 6. Dez. 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 (6.650 Wörter) - 10:28, 7. Dez. 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) - 00:52, 30. Okt. 2025
- settings folded with the number can be changed without changing the result. The square root of 10 is of important in order-of-magnitude calculations and estimates…16 KB (2.146 Wörter) - 13:47, 16. Dez. 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