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Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
A complex number that includes also the extraction of cube roots has a solid construction. In the language of fields, a complex number that is planar has degree a power of two, and lies in a field extension that can be broken down into a tower of fields where each extension has degree two. A complex number that has a solid construction has ...
Also, the use of principal cube root may give a wrong result if the coefficients are non-real complex numbers. Moreover, if the coefficients belong to another field, the principal cube root is not defined in general. The second way for making Cardano's formula always correct, is to remark that the product of the two cube roots must be –p / 3 ...
Constructible number. The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length can be constructed with compass and ...
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system that extends ...
The imaginary unit i in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis. The imaginary unit or unit imaginary number ( i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to ...
In mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where x is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x is a number r (the root ...
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves.