60 relations: Absolute value, Addition, Additive inverse, Algebraic closure, Argument (complex analysis), Automorphism, Biquaternion, Bivector (complex), Branch point, Cartesian coordinate system, Circle group, Complex conjugate, Complex logarithm, Complex number, Complex plane, Complex-valued function, Control engineering, Electric current, Electrical engineering, Equating coefficients, Euler's formula, Factorial, Field (mathematics), Fundamental theorem of algebra, Galois group, Gamma function, Identity matrix, Imaginary number, Integer, Iota, Isomorphism, Mathematics, MATLAB, Modulo operation, Multiplication, Multiplicative inverse, Multiplicity (mathematics), Multivalued function, Nth root, Orthogonal group, Polynomial, Principal value, Python (programming language), Quadratic equation, Quadratic function, Quaternion, Real number, Regular polygon, Riemann surface, Root of unity, ..., Sine, Square (algebra), Square root, Trigonometric functions, Uniqueness quantification, Unit circle, Up to, Well-defined, Zero of a function, 0. Expand index (10 more) »

## Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

New!!: Imaginary unit and Absolute value · See more »

## Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

New!!: Imaginary unit and Addition · See more »

## Additive inverse

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

New!!: Imaginary unit and Additive inverse · See more »

## Algebraic closure

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.

New!!: Imaginary unit and Algebraic closure · See more »

## Argument (complex analysis)

In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.

New!!: Imaginary unit and Argument (complex analysis) · See more »

## Automorphism

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

New!!: Imaginary unit and Automorphism · See more »

## Biquaternion

In abstract algebra, the biquaternions are the numbers, where, and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group.

New!!: Imaginary unit and Biquaternion · See more »

## Bivector (complex)

In mathematics, a bivector is the vector part of a biquaternion.

New!!: Imaginary unit and Bivector (complex) · See more »

## Branch point

In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.

New!!: Imaginary unit and Branch point · See more »

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

New!!: Imaginary unit and Cartesian coordinate system · See more »

## Circle group

In mathematics, the circle group, denoted by T, 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 The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.

New!!: Imaginary unit and Circle group · See more »

## 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.

New!!: Imaginary unit and Complex conjugate · See more »

## Complex logarithm

In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which.

New!!: Imaginary unit and Complex logarithm · See more »

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

New!!: Imaginary unit and Complex number · See more »

## Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

New!!: Imaginary unit and Complex plane · See more »

## Complex-valued function

In mathematics, a complex-valued function (not to be confused with complex variable function) is a function whose values are complex numbers.

New!!: Imaginary unit and Complex-valued function · See more »

## Control engineering

Control engineering or control systems engineering is an engineering discipline that applies automatic control theory to design systems with desired behaviors in control environments.

New!!: Imaginary unit and Control engineering · See more »

## Electric current

An electric current is a flow of electric charge.

New!!: Imaginary unit and Electric current · See more »

## Electrical engineering

Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism.

New!!: Imaginary unit and Electrical engineering · See more »

## 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.

New!!: Imaginary unit and Equating coefficients · See more »

## 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.

New!!: Imaginary unit and Euler's formula · See more »

## Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

New!!: Imaginary unit and Factorial · See more »

## Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

New!!: Imaginary unit and Field (mathematics) · See more »

## Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

New!!: Imaginary unit and Fundamental theorem of algebra · See more »

## Galois group

In mathematics, more specifically 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.

New!!: Imaginary unit and Galois group · See more »

## Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

New!!: Imaginary unit and Gamma function · See more »

## Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

New!!: Imaginary unit and Identity matrix · See more »

## Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.

New!!: Imaginary unit and Imaginary number · See more »

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

New!!: Imaginary unit and Integer · See more »

## Iota

Iota (uppercase Ι, lowercase ι) is the ninth letter of the Greek alphabet.

New!!: Imaginary unit and Iota · See more »

## Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

New!!: Imaginary unit and Isomorphism · See more »

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Imaginary unit and Mathematics · See more »

## MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

New!!: Imaginary unit and MATLAB · See more »

## Modulo operation

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus).

New!!: Imaginary unit and Modulo operation · See more »

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

New!!: Imaginary unit and Multiplication · See more »

## 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.

New!!: Imaginary unit and Multiplicative inverse · See more »

## Multiplicity (mathematics)

In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.

New!!: Imaginary unit and Multiplicity (mathematics) · See more »

## Multivalued function

In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.

New!!: Imaginary unit and Multivalued function · See more »

## Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

New!!: Imaginary unit and Nth root · See more »

## Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

New!!: Imaginary unit and Orthogonal group · See more »

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

New!!: Imaginary unit and Polynomial · See more »

## Principal value

In 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.

New!!: Imaginary unit and Principal value · See more »

## Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

New!!: Imaginary unit and Python (programming language) · See more »

## Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

New!!: Imaginary unit and Quadratic equation · See more »

## Quadratic function

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

New!!: Imaginary unit and Quadratic function · See more »

## Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

New!!: Imaginary unit and Quaternion · See more »

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

New!!: Imaginary unit and Real number · See more »

## Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

New!!: Imaginary unit and Regular polygon · See more »

## Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

New!!: Imaginary unit and Riemann surface · See more »

## Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.

New!!: Imaginary unit and Root of unity · See more »

## Sine

In mathematics, the sine is a trigonometric function of an angle.

New!!: Imaginary unit and Sine · See more »

## Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

New!!: Imaginary unit and Square (algebra) · See more »

## Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

New!!: Imaginary unit and Square root · See more »

## Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

New!!: Imaginary unit and Trigonometric functions · See more »

## Uniqueness quantification

In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists.

New!!: Imaginary unit and Uniqueness quantification · See more »

## Unit circle

In mathematics, a unit circle is a circle with a radius of one.

New!!: Imaginary unit and Unit circle · See more »

## Up to

In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.

New!!: Imaginary unit and Up to · See more »

## Well-defined

In mathematics, an expression is called well-defined or unambiguous if its definition assigns it a unique interpretation or value.

New!!: Imaginary unit and Well-defined · See more »

## 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, x is a solution of the equation f(x).

New!!: Imaginary unit and Zero of a function · See more »

## 0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

New!!: Imaginary unit and 0 · See more »

## Redirects here:

Complex Unit, I (imaginary unit), I (mathematical constant), I (number), I^i, Sqrt -1, Sqrt(-1), Sqrt(−1), Square root of -1, Square root of minus one, Square root of –1, Square root of −1, Unit imaginary number, ⅈ, ⅉ, √-1, √−1.

## References

[1] https://en.wikipedia.org/wiki/Imaginary_unit