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# Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation. 

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, ... 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.

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

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

## Algebraic closure

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

## Argument (complex analysis)

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

## Automorphism

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

## 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.

## Bivector (complex)

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

## 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.

## 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.

## 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&times;, the multiplicative group of all nonzero complex numbers.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## Electric current

An electric current is a flow of electric charge.

## Electrical engineering

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

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Iota

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

## 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.

## Mathematics

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

## MATLAB

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

## Modulo operation

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

## 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.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## Multiplicity (mathematics)

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

## Multivalued function

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

## 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.

## 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.

## 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.

## 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.

## Python (programming language)

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

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.

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.

## Quaternion

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

## Real number

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

## 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).

## Riemann surface

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

## 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.

## Sine

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

## Square (algebra)

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

## 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.

## Trigonometric functions

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

## 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.

## Unit circle

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

## 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.

## Well-defined

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

## 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).

## 0

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

## References

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