field of complex numbers C

URI: https://gptkb.org/entity/field_of_complex_numbers_C

GPTKB entity

Statements (50)

Predicate	Object
gptkbp:instanceOf	gptkb:algebra gptkb:Field
gptkbp:algebraic_closure_of	field of real numbers
gptkbp:automorphismGroup	complex conjugation
gptkbp:basis_over	{1, i} over real numbers
gptkbp:cardinality	continuum
gptkbp:characteristic	0
gptkbp:contains	rational numbers real numbers algebraic numbers transcendental numbers imaginary numbers
gptkbp:containsElement	i (imaginary unit)
gptkbp:dimension_over	2 over real numbers
gptkbp:Galois_group_over_real_numbers	order 2 generated by complex conjugation
https://www.w3.org/2000/01/rdf-schema#label	field of complex numbers C
gptkbp:is_a_Banach_space	true
gptkbp:is_a_commutative_field	true
gptkbp:is_a_division_algebra_over	real numbers
gptkbp:is_a_field_extension_of	rational numbers real numbers integers
gptkbp:is_a_Galois_extension_of	real numbers
gptkbp:is_a_Hilbert_space	true
gptkbp:is_a_metric_space	true
gptkbp:is_a_normed_space	true
gptkbp:is_a_splitting_field_of	all polynomials over rational numbers all polynomials over real numbers x^2 + 1 over real numbers
gptkbp:is_a_topological_field	true
gptkbp:is_a_vector_space_over	rational numbers real numbers
gptkbp:is_algebraically_closed	true
gptkbp:is_complete	true
gptkbp:is_not_formally_real	true
gptkbp:is_not_ordered	true
gptkbp:minimal_polynomial_of_i	x^2 + 1
gptkbp:represents	a + bi, where a, b are real numbers
gptkbp:symbol	ℂ
gptkbp:topology	gptkb:Euclidean_topology
gptkbp:used_in	gptkb:algebra gptkb:geometry gptkb:signal_processing complex analysis engineering physics quantum mechanics
gptkbp:bfsParent	gptkb:infinite_field_F
gptkbp:bfsLayer	7