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A cube root of a number x is a number y such that y3 = x. Learn about the real and complex cube roots, their formal definition, geometric representation, numerical methods and applications in mathematics.
An nth root of a number x is a number r that, when raised to the power of n, yields x. The number x is called the radicand and the index or degree of the root is n. Learn more about the history, notation, properties and operations of nth roots.
A cube is the third power of a number, denoted by a superscript 3. Learn about the cube function, the cube root, the cubic parabola, and the perfect cubes in integers and base ten.
A root of unity is a complex number that yields 1 when raised to some positive integer power n. Learn about the definition, properties, and examples of roots of unity in different fields and rings.
Learn about the origins and solutions of cubic equations, which are equations of the form ax3 + bx2 + cx + d = 0. Find out how ancient and medieval mathematicians from different cultures approached and solved cubic equations using algebra, geometry, and numerical approximations.
An algebraic number field is a finite-dimensional extension field of the rational numbers. Learn about its definition, examples, properties, and applications in algebraic number theory.
Similarly, in 1844 while working on cubic reciprocity, Eisenstein introduced the ring [], where = +, = is a cube root of unity. This is the ring of Eisenstein integers , and he proved it has the six units ± 1 , ± ω , ± ω 2 {\displaystyle \pm 1,\pm \omega ,\pm \omega ^{2}} and that it has unique factorization.
The imaginary unit i is a solution to the quadratic equation x2 + 1 = 0 and a fundamental part of complex numbers. Learn about its history, notation, representation, matrices, roots and applications in mathematics and engineering.