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Imaginary unit

The term imaginary unit or unit imaginary number refers to a solution to the equation. [1]

62 relations: Absolute value, Addition, Additive inverse, Algebraic closure, Argument (complex analysis), Associative property, Automorphism, Biquaternion, Bivector (complex), Branch point, Cartesian coordinate system, Circle group, Closure (mathematics), Commutative property, Complex conjugate, Complex logarithm, Complex number, Complex plane, Complex-valued function, Control engineering, Distributive property, 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, Matrix (mathematics), Modulo operation, Multiplication, Multiplicative inverse, Multiplicity (mathematics), Multivalued function, Nth root, Orthogonal group, Polynomial, Principal value, Python (programming language), Quadratic function, Quaternion, ..., Real number, Riemann surface, Root of unity, Square (algebra), Square root, Uniqueness quantification, Unit circle, Up to, Well-defined, Zero of a function, 0 (number), 2 × 2 real matrices. Expand index (12 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.

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Addition

Addition (often signified by the plus symbol "+") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.

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Additive inverse

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

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Algebraic closure

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

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Argument (complex analysis)

In mathematics, arg is a function operating on complex numbers (visualized in a complex plane).

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Automorphism

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

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Biquaternion

In abstract algebra, the biquaternions are the numbers, where w, x, y, and z are complex numbers and the elements of multiply as in the quaternion group.

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Bivector (complex)

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

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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.

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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 from the point to two fixed perpendicular directed lines, measured in the same unit of length.

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Circle group

In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., 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.

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Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Complex conjugate

In mathematics, the complex conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign.

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Complex logarithm

In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the real natural logarithm ln x is the inverse of the real exponential function ex.

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Complex number

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

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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 orthogonal imaginary axis.

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Complex-valued function

In mathematics, a complex-valued function (sometimes referred to as complex function) is a function whose values are complex numbers.

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Control engineering

Control engineering or control systems engineering is the engineering discipline that applies control theory to design systems with desired behaviors.

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Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from elementary algebra.

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Electric current

An electric current is a flow of electric charge.

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Electrical engineering

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

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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.

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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.

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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.

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Field (mathematics)

In abstract algebra, a field is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

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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.

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Galois group

In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

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Gamma function

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

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Identity matrix

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

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Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is often used in Engineering which is defined by its property.

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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").

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Iota

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

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Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism (or more generally a morphism) that admits an inverse.

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Mathematics

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

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MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and fourth-generation programming language.

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Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is interpreted and manipulated in certain prescribed ways.

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Modulo operation

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

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "·" or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.

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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.

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Multiplicity (mathematics)

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

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Multivalued function

In mathematics, a multivalued function (short form: multifunction; other names: many-valued function, set-valued function, set-valued map, point-to-set map, multi-valued map, multimap, correspondence, carrier) is a left-total relation (that is, every input is associated with at least one output) in which at least one input is associated with multiple (two or more) outputs.

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Nth root

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

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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.

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Polynomial

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

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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.

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Python (programming language)

Python is a widely used general-purpose, high-level programming language.

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Quadratic function

In mathematics, 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.

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Quaternion

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

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Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold.

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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.

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Square (algebra)

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

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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.

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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.

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Unit circle

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

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Up to

In mathematics, the phrase up to indicates that its grammatical object is some equivalence class, to be regarded as a single entity, or disregarded as a single entity.

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Well-defined

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

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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 In other words, a "zero" of a function is an input value that produces an output of zero (0).

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0 (number)

0 (zero; BrE: or AmE) is both a number and the numerical digit used to represent that number in numerals.

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2 × 2 real matrices

In mathematics, the set of real matrices is denoted by M(2, R).

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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, , , √-1, √−1.

References

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

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