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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 with opposite sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is ⁠ a − b i {\displaystyle a-bi} ⁠. The complex conjugate of…

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Properties

Distributive Fixed points Involution Multiplicative inverse Commutative

16 related topics

Generalizations

Dual numbers Split-complex numbers Adjoint operator Hilbert spaces C*-algebras

13 related topics

Notation

Vinculum Conjugate transpose Matrix Physics Dagger

10 related topics

Use as a variable

Modulus (or absolute value)Argument Frank Morley

3 related topics

Topics to explore

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Overview

Mathematics
Complex number
Real Real number
Imaginary Imaginary number
Magnitude Magnitude of a complex number
Sign Sign (mathematics)
Polar coordinates Polar coordinate system
Euler's formula
Univariate
Complex conjugate is also a root Complex conjugate root theorem

Notation

Properties

Distributive Distributive property
Fixed points Fixed point (mathematics)
Involution Involution (mathematics)
Multiplicative inverse
Commutative
Polynomial
Holomorphic Holomorphic function
Homeomorphism
Antilinear
Vector space
Well-behaved
Bijective
Field Field (mathematics)
Automorphism
Galois group
Field extension

Use as a variable

Modulus (or absolute value) Absolute value
Argument Argument (complex analysis)
Frank Morley

Generalizations

Dual numbers
Split-complex numbers Split-complex number
Adjoint operator
Hilbert spaces Hilbert space
C*-algebras C*-algebra
Quaternions Quaternion
Split-quaternions Split-quaternion
Vector spaces
Antilinear map
Identity map
Real structure
Vectors Vector (mathematics and physics)
Canonical Canonical form

Bibliography

Budinich, P. Paolo Budinich
Trautman, A. Andrzej Trautman
ISBN ISBN (identifier)

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Map overview Semantic statistics

Complex conjugate

Nodes62

Edges61

Triples11

Avg. degree1.97

Density0.032258

Components1

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Complex conjugate

Top relations

see also · 7

Complex conjugate → Absolute, Change, Concept, Mathematics, Operation, Product, Type

related to Notation · 4

Complex conjugate → Boolean, If, NOT, The

Important terminology Word statistics

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Important terminology

complex displaystyle real conjugate overline number conjugation numbers left right mathbb textstyle varphi also transpose antilinear vector mathematics imaginary frac

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Complex conjugate	related to Notation	The	0.60	section
Complex conjugate	related to Notation	NOT	0.60	section
Complex conjugate	related to Notation	Boolean	0.60	section
Complex conjugate	related to Notation	If	0.60	section
Complex conjugate	see also	Absolute	0.60	section
Complex conjugate	see also	Product	0.60	section
Complex conjugate	see also	Operation	0.60	section
Complex conjugate	see also	Mathematics	0.60	section
Complex conjugate	see also	Type	0.60	section
Complex conjugate	see also	Change	0.60	section
Complex conjugate	see also	Concept	0.60	section

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