Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
C
set of complex numbers |
| gptkbp:automorphismGroup |
complex conjugation
|
| gptkbp:basisOverR |
{1, i}
|
| gptkbp:canBe |
ordered pairs of real numbers
points in the complex plane polar coordinates (r, θ) |
| gptkbp:cardinality |
continuum
|
| gptkbp:characteristic |
0
|
| gptkbp:consistsOf |
numbers of the form a + bi
|
| gptkbp:contains |
real numbers
imaginary numbers pure imaginary numbers |
| gptkbp:dimensionOverR |
2
|
| gptkbp:firstDefined |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:form |
gptkb:topology
gptkb:C*-algebra algebraically closed field division algebra over the real numbers quadratic extension of the real numbers topological field |
| gptkbp:hasNoOrder |
cannot be totally ordered as a field
|
| https://www.w3.org/2000/01/rdf-schema#label |
the complex numbers C
|
| gptkbp:importantElement |
0
1 i -1 -i |
| gptkbp:introducedIn |
16th century mathematics
|
| gptkbp:isAlgebraicClosureOf |
the real numbers R
|
| gptkbp:isomorphicTo |
R^2 as a real vector space
|
| gptkbp:location |
a and b are real numbers
i is the imaginary unit |
| gptkbp:operator |
addition
essay multiplication modulus conjugation |
| gptkbp:property |
commutative ring
algebraically closed field 2-dimensional vector space over the real numbers contains the imaginary unit i, where i^2 = -1 contains the real numbers as a subfield field extension of the real numbers |
| gptkbp:symbol |
ℂ
|
| gptkbp:topology |
gptkb:Euclidean_topology
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:geometry gptkb:signal_processing complex analysis electrical engineering quantum mechanics |
| gptkbp:bfsParent |
gptkb:the_ring_of_integers_Z
|
| gptkbp:bfsLayer |
7
|