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Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 {\displaystyle i^{2}=-1} . Since no real number satisfies the above equation, i was called an imaginary number by René Descartes. Every complex number can be…

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Overview

Definition and basic operations

History

Abstract and algebraic definitions

Complex analysis

Applications

Characterizations, generalizations and related notions

Advanced semantic analysis

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Map overview Semantic statistics

Complex number

Nodes317
Edges316
Triples116
Avg. degree1.99
Density0.006309
Components1

How this topic connects Entity context

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Complex number

Top relations

related to Fundamental theorem of algebra · 11
Complex number → Alembert, Because, Carl Friedrich Gauss, Galois, It, Jean, Liouville's, Rond, The, There, This
related to history · 11
Complex number → Ars Magna, Because, Cardano, Complex, Ferro, Gerolamo Cardano, Italian, Scipione, The, This, Work
related to Other number systems · 9
Complex number → Applying, By Hurwitz's, Cayley, Dickson, In, Passing, The, This, Unlike
related to Construction as a quotient ring · 7
Complex number → Basic, However, One, Since, The, This, To
related to Complex conjugate, absolute value, argument and division · 5
Complex number → Conjugating, For, Geometrically, It, The
related to Linear algebra · 5
Complex number → By, Complex, For, Since, The
related to Powers and roots · 5
Complex number → Because, For, Here, Moivre's, The
related to Analytic number theory · 4
Complex number → Analytic, For, Riemann, This
related to Complex logarithm · 4
Complex number → Euler's, For, The, This
related to Definition and basic operations · 4
Complex number → For, Im, Re, The

Important terminology Word statistics

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Important terminology

complex displaystyle numbers real number mathbb field form one imaginary called equation plane functions example cos value used two sin

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Complex numberis aelement of a number system that extends the real numbers with a specific element denoted i0.90text
Complex numberis asimilarity centered at the origin0.90text
Complex numberis aexpression of the form a0.90text
electromagnetisminstance ofIn some disciplines0.80text
electrical engineeringinstance ofIn some disciplines0.80text
j is used instead of iinstance ofIn some disciplines0.80text
as i frequently represents electric currentinstance ofIn some disciplines0.80text
and complex numbers are written as ainstance ofIn some disciplines0.80text
Liouville's theoreminstance ofby either analytic methods0.80text
or topological ones such as the winding numberinstance ofby either analytic methods0.80text
or a proof combining Galois theoryinstance ofby either analytic methods0.80text
the fact that any real polynomial of odd degree has at least one real root.The field of complex numbers is defined as theinstance ofby either analytic methods0.80text

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    Min side: 3
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