Table of Contents
92 relations: Absolute value, Addition, Additive inverse, Algebra, Algebraic closure, American Scientist, Argument (complex analysis), Automorphism, Bivector, Branch point, Cartesian coordinate system, Circle group, Clockwise, Coefficient, Complex conjugate, Complex logarithm, Complex number, Complex plane, Control engineering, Cube root, Cyclic group, Cylinder, Determinant, Electric current, Electrical engineering, Equating coefficients, Euclidean plane, Euclidean space, Euclidean vector, Euler's formula, Even and odd functions, Exponential function, Factorial, Field (mathematics), Fundamental theorem of algebra, Galois group, Gamma function, Gamma matrices, Gaussian integer, Geometric algebra, Group (mathematics), Hermann Grassmann, Hyperbolic functions, Ideal (ring theory), Identity function, Identity matrix, Imaginary number, Integer, Isaac Newton, Isomorphism, ... Expand index (42 more) »
- Algebraic numbers
- Complex numbers
- Quadratic irrational numbers
Absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign.
See Imaginary unit and Absolute value
Addition
Addition (usually signified by the plus symbol) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.
See Imaginary unit and Addition
Additive inverse
In mathematics, the additive inverse of a number (sometimes called the opposite of) is the number that, when added to, yields zero.
See Imaginary unit and Additive inverse
Algebra
Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures.
See Imaginary unit and Algebra
Algebraic closure
In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.
See Imaginary unit and Algebraic closure
American Scientist
American Scientist (informally abbreviated AmSci) is an American bimonthly science and technology magazine published since 1913 by Sigma Xi, The Scientific Research Honor Society.
See Imaginary unit and American Scientist
Argument (complex analysis)
In mathematics (particularly in complex analysis), the argument of a complex number, denoted, is the angle between the positive real axis and the line joining the origin and, represented as a point in the complex plane, shown as \varphi in Figure 1.
See Imaginary unit and Argument (complex analysis)
Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
See Imaginary unit and Automorphism
Bivector
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.
See Imaginary unit and Bivector
Branch point
In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values) at that point, all of its neighborhoods contain a point that has more than n values.
See Imaginary unit and Branch point
Cartesian coordinate system
In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.
See Imaginary unit and Cartesian coordinate system
Circle group
In mathematics, the circle group, denoted by \mathbb T or, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers \mathbb T.
See Imaginary unit and Circle group
Clockwise
Two-dimensional rotation can occur in two possible directions or senses of rotation.
See Imaginary unit and Clockwise
Coefficient
In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression.
See Imaginary unit and Coefficient
Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. Imaginary unit and complex conjugate are complex numbers.
See Imaginary unit and Complex conjugate
Complex logarithm
In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers.
See Imaginary unit and Complex logarithm
Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^. Imaginary unit and complex number are complex numbers.
See Imaginary unit and Complex number
Complex plane
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, called the imaginary axis, is formed by the imaginary numbers. Imaginary unit and complex plane are complex numbers.
See Imaginary unit and Complex plane
Control engineering
Control engineering or control systems engineering or Automation engineering (In Some European Countries) is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments.
See Imaginary unit and Control engineering
Cube root
In mathematics, a cube root of a number is a number such that.
See Imaginary unit and Cube root
Cyclic group
In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently \Zn or Zn, not to be confused with the commutative ring of p-adic numbers), that is generated by a single element.
See Imaginary unit and Cyclic group
Cylinder
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
See Imaginary unit and Cylinder
Determinant
In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.
See Imaginary unit and Determinant
Electric current
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space.
See Imaginary unit and Electric current
Electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism.
See Imaginary unit and Electrical engineering
Equating coefficients
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters.
See Imaginary unit and Equating coefficients
Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.
See Imaginary unit and Euclidean plane
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space.
See Imaginary unit and Euclidean space
Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction.
See Imaginary unit and Euclidean vector
Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
See Imaginary unit and Euler's formula
Even and odd functions
In mathematics, an even function is a real function such that f(-x).
See Imaginary unit and Even and odd functions
Exponential function
The exponential function is a mathematical function denoted by f(x).
See Imaginary unit and Exponential function
Factorial
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &.
See Imaginary unit and Factorial
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.
See Imaginary unit and Field (mathematics)
Fundamental theorem of algebra
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
See Imaginary unit and Fundamental theorem of algebra
Galois group
In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
See Imaginary unit and Galois group
Gamma function
In mathematics, the gamma function (represented by, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers.
See Imaginary unit and Gamma function
Gamma matrices
In mathematical physics, the gamma matrices, \ \left\\, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra \ \mathrm_(\mathbb) ~. It is also possible to define higher-dimensional gamma matrices.
See Imaginary unit and Gamma matrices
Gaussian integer
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. Imaginary unit and Gaussian integer are algebraic numbers, complex numbers and quadratic irrational numbers.
See Imaginary unit and Gaussian integer
Geometric algebra
In mathematics, a geometric algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors.
See Imaginary unit and Geometric algebra
Group (mathematics)
In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.
See Imaginary unit and Group (mathematics)
Hermann Grassmann
Hermann Günther Grassmann (Graßmann,; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician.
See Imaginary unit and Hermann Grassmann
Hyperbolic functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle.
See Imaginary unit and Hyperbolic functions
Ideal (ring theory)
In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements.
See Imaginary unit and Ideal (ring theory)
Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged.
See Imaginary unit and Identity function
Identity matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere.
See Imaginary unit and Identity matrix
Imaginary number
An imaginary number is the product of a real number and the imaginary unit, is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property. Imaginary unit and imaginary number are complex numbers.
See Imaginary unit and Imaginary number
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
See Imaginary unit and Integer
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher.
See Imaginary unit and Isaac Newton
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.
See Imaginary unit and Isomorphism
Leonhard Euler
Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.
See Imaginary unit and Leonhard Euler
Matrix (mathematics)
In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
See Imaginary unit and Matrix (mathematics)
Matrix multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices.
See Imaginary unit and Matrix multiplication
Multiplication
Multiplication (often denoted by the cross symbol, by the mid-line dot operator, by juxtaposition, or, on computers, by an asterisk) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division.
See Imaginary unit and Multiplication
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
See Imaginary unit and Multiplicative inverse
Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
See Imaginary unit and Multiplicity (mathematics)
Multivalued function
In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least one point in its domain.
See Imaginary unit and Multivalued function
Negative number
In mathematics, a negative number represents an opposite.
See Imaginary unit and Negative number
Neil Sloane
Neil James Alexander Sloane FLSW (born October 10, 1939) is a British-American mathematician.
See Imaginary unit and Neil Sloane
Nth root
In mathematics, an th root of a number is a number (the root) which, when raised to the power of the positive integer, yields: r^n.
See Imaginary unit and Nth root
Number line
In elementary mathematics, a number line is a picture of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.
See Imaginary unit and Number line
On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences.
See Imaginary unit and On-Line Encyclopedia of Integer Sequences
Partial fraction decomposition
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
See Imaginary unit and Partial fraction decomposition
Polynomial
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
See Imaginary unit and Polynomial
Principal value
In mathematics, specifically complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.
See Imaginary unit and Principal value
Quadratic equation
In mathematics, a quadratic equation is an equation that can be rearranged in standard form as ax^2 + bx + c.
See Imaginary unit and Quadratic equation
Quadratic function
In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables.
See Imaginary unit and Quadratic function
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics.
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
See Imaginary unit and Real number
Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
See Imaginary unit and Regular polygon
René Descartes
René Descartes (or;; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science.
See Imaginary unit and René Descartes
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold.
See Imaginary unit and Riemann surface
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist.
See Imaginary unit and Ring (mathematics)
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power. Imaginary unit and root of unity are algebraic numbers and complex numbers.
See Imaginary unit and Root of unity
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.
See Imaginary unit and Similarity (geometry)
Split-complex number
In algebra, a split complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit satisfying j^2.
See Imaginary unit and Split-complex number
Square (algebra)
In mathematics, a square is the result of multiplying a number by itself.
See Imaginary unit and Square (algebra)
Square lattice
In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.
See Imaginary unit and Square lattice
Square root
In mathematics, a square root of a number is a number such that y^2.
See Imaginary unit and Square root
The American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
See Imaginary unit and The American Mathematical Monthly
Trace (linear algebra)
In linear algebra, the trace of a square matrix, denoted, is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of.
See Imaginary unit and Trace (linear algebra)
Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
See Imaginary unit and Translation (geometry)
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
See Imaginary unit and Trigonometric functions
Uniqueness quantification
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition.
See Imaginary unit and Uniqueness quantification
Unit circle
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1.
See Imaginary unit and Unit circle
Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
See Imaginary unit and Unit vector
Up to
Two mathematical objects and are called "equal up to an equivalence relation ".
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.
See Imaginary unit and Wiley (publisher)
William Kingdon Clifford
William Kingdon Clifford (4 May 18453 March 1879) was a British mathematician and philosopher.
See Imaginary unit and William Kingdon Clifford
Zero of a function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).
See Imaginary unit and Zero of a function
0
0 (zero) is a number representing an empty quantity.
1
1 (one, unit, unity) is a number representing a single or the only entity.
See also
Algebraic numbers
- Algebraic integer
- Algebraic number
- Chebyshev nodes
- Constructible number
- Eisenstein integer
- Fundamental theorem of ideal theory in number fields
- Gaussian integer
- Geometric Constructions
- Hard hexagon model
- Imaginary unit
- Look-and-say sequence
- Perron number
- Pisot–Vijayaraghavan number
- Principal root of unity
- Quadratic irrational numbers
- Rational numbers
- Root of unity
- Roth's theorem
- Salem number
- Twelfth root of two
Complex numbers
- Algebraic numbers
- CM-field
- Caspar Wessel
- Complex analysis
- Complex conjugate
- Complex conjugate line
- Complex measure
- Complex number
- Complex plane
- Complex-base system
- External ray
- Gaussian integer
- Gaussian moat
- Hypercomplex numbers
- Imaginary number
- Imaginary unit
- Jean-Robert Argand
- Mean value problem
- Principal root of unity
- Quater-imaginary base
- Real numbers
- Root of unity
- Table of Gaussian integer factorizations
- Transcendental numbers
Quadratic irrational numbers
- Eisenstein integer
- Gaussian integer
- Golden ratio
- Imaginary unit
- Kleinian integer
- Lieb's square ice constant
- Quadratic irrational number
- Silver ratio
- Square root of 2
- Square root of 3
- Square root of 5
- Square root of 6
- Square root of 7
References
Also known as Complex Unit, I (imaginary unit), I (mathematical constant), I (number), I^i, Imaginary constant, Sqrt -1, Sqrt(-1), Square root of -1, Square root of minus one, Square root of negative one, Unit imaginary number, Unit lateral number, .