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a complex line is a one-dimensional affine subspace of a vector space over the complex numbers. A common point of confusion is that while a complex line
Complex_line
Definite integral of a scalar or vector field along a path
reserved for line integrals in the complex plane. The function to be integrated may be a scalar field or a vector field. The value of the line integral is
Line_integral
Vector bundle of rank 1
having a two-point fiber, the unit interval as a fiber, or the real line. Complex line bundles are closely related to circle bundles. There are some celebrated
Line_bundle
In algebraic geometry, a line complex is a set of lines that can be specified by a list of homogeneous polynomial equations. That is, a projective variety
Line_complex
Geometric representation of the complex numbers
function in the complex plane. The lengths of straight lines and curves in the complex plane represent real numbers: the physical length of the line or curve
Complex_plane
2D surface which extends indefinitely
structure, one may view the plane as a 1-dimensional complex manifold, called the complex line. Many fundamental tasks in mathematics, geometry, trigonometry
Plane_(mathematics)
Model of the extended complex plane plus a point at infinity
Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. This extended
Riemann_sphere
Mathematical concept
In topology, the complex projective space plays an important role as a classifying space for complex line bundles: families of complex lines parametrized
Complex_projective_space
Kind of complex manifold
In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian
Complex_torus
Concept in geometry
to the complex line (which may be thought of as the complex plane), thereby turning it into a closed surface known as the complex projective line, CP1,
Point_at_infinity
Theorem in complex analysis
Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic
Cauchy's_integral_theorem
Characteristic classes of vector bundles
actually copies of the real line), there are generalizations in which the hairs are complex (see the example of the complex hairy ball theorem below),
Chern_class
Type of mathematical functions
theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space C n {\displaystyle
Function of several complex variables
Function_of_several_complex_variables
Topics referred to by the same term
sets Chain complex, an algebraic structure Simplicial complex, a kind of topological space CW complex, a kind of topological space Line complex, a 3-dimensional
Complex
Space formed by the ''n''-tuples of complex numbers
{\displaystyle \mathbb {C} ^{n}} , and is the n-fold Cartesian product of the complex line C {\displaystyle \mathbb {C} } with itself. Symbolically, C n = { ( z
Complex_coordinate_space
Operation in complex geometry
In complex geometry, the complex conjugate line of a straight line is the line that it becomes by taking the complex conjugate of each point on this line
Complex_conjugate_line
Number with a real and an imaginary part
expressed in terms of complex numbers. For example, the real numbers form the real line, which is pictured as the horizontal axis of the complex plane, while real
Complex_number
Generalization of a polytope in real space
line of multiple planes, and so on. Precise definitions exist only for the regular complex polytopes, which are configurations. The regular complex polytopes
Complex_polytope
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
obtained using the complex projective line, C P 1 {\displaystyle \mathbb {CP} ^{1}} , which is defined to be the set of all complex one-dimensional subspaces
Hopf_fibration
Concept in geometry and topology
at the line at infinity. The analogue for the complex projective plane is a 'line' at infinity that is (naturally) a complex projective line. Topologically
Line_at_infinity
Property of a differential manifold that includes complex structures
geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic
Generalized_complex_structure
Type of mathematical set
In mathematics, a simplicial complex is a structured set of simplices (for example, points, line segments, triangles, and their n-dimensional counterparts)
Simplicial_complex
ball of C n {\displaystyle \mathbb {C} ^{n}} , because every negative complex line is spanned by a unique vector of the form ( 1 , x 1 , … , x n ) {\displaystyle
Complex_hyperbolic_space
Interference pattern
at a faster speed. This effect is called optical moiré speedup. More complex line moiré patterns are created if the lines are curved or not exactly parallel
Moiré_pattern
infinite dimensional complex projective space, which is the classifying space for complex line bundles, so that tensor product of line bundles induces a
Complex_cobordism
Three or more adults in a partnership
created specific types of group marriages for The Moon Is a Harsh Mistress (line marriage) and Friday (S-groups). In several of her Hainish Cycle stories
Group_marriage
Construction for vector bundles
if a real line bundle is orientable, both conditions are then equivalent to a trivial determinant line bundle. The complex determinant line bundle preserves
Determinant_line_bundle
Algebraic topology theory
viewed as a bijection between the set of all isomorphism classes of complex line bundles on a manifold M and H 2 ( M ; Z ) . {\displaystyle H^{2}(M;\mathbb
Equivariant_cohomology
New York City Subway station in Brooklyn
City Subway station complex shared by the elevated BMT Canarsie Line and BMT Jamaica Line, and the underground IND Fulton Street Line. It was also served
Broadway_Junction_station
One-dimensional complex manifold
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied
Riemann_surface
In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be viewed as a real vector
Complex_vector_bundle
Study of complex manifolds and several complex variables
complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Principal fiber bundle
a smooth complex line bundle (essentially because a circle is homotopically equivalent to C ∗ {\displaystyle \mathbb {C} ^{*}} , the complex plane with
Circle_bundle
Angle of complex number about real axis
(particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the
Argument_(complex_analysis)
Fundamental operation on complex numbers
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 opposite in
Complex_conjugate
Train station in South Korea
Gasan Digital Complex Station (Korean: 가산디지털단지역) is on Gyeongbu Line, Seoul Metropolitan Subway Line 1 and Seoul Metropolitan Subway Line 7. Its former
Gasan_Digital_Complex_station
Branch of mathematics studying functions of a complex variable
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions
Complex_analysis
Mathematical object studied in the field of algebraic geometry
(In the classical topology coming from the topology on the complex numbers, a complex line is a real manifold of dimension two.) This is the set Z(f):
Algebraic_variety
Polygons which have an accompanying imaginary dimension for each real dimension
understood as a collection of complex points, lines, planes, and so on, where every point is the junction of multiple lines, every line of multiple planes, and
Regular_complex_polygon
Method of evaluating certain integrals along paths in the complex plane
integrals of functions over the real line. Regarding the real line as a contour, and deforming it into the complex plane often leads to simpler integrals
Contour_integration
Comedy by Aristophanes
Sicily, reflected in the accusation of the cheese theft. Philocleon is a complex character whose actions have comic significance, psychological significance
The_Wasps
Pseudometric of complex manifolds
every holomorphic map from the complex line C to X is constant. The origins of the concept lie in Schwarz's lemma in complex analysis. Namely, if f is a
Kobayashi_metric
Logarithm of a complex number
k} . These logarithms are equally spaced along a vertical line in the complex plane. A complex-valued function log : U → C {\displaystyle \log \colon U\to
Complex_logarithm
Mathematical technique for vector bundles
characteristic classes for complex vector bundles correspond to symmetric polynomials in the first Chern classes of complex line bundles; these are the Chern
Splitting_principle
Affine space over the complex numbers
is, a complex line through the origin of X). But if c is some non-zero complex number, then the set A of solutions of α(x) = c is an affine line in X,
Complex_affine_space
Concept in differential geometry
a trivial line bundle if the manifold is odd-dimensional. Yet another definition is that a spinC structure on a manifold N is a complex line bundle L over
Spin_structure
Theorem in algebraic geometry
Abhyankar–Moh theorem states that if L {\displaystyle L} is a complex line in the complex affine plane C 2 {\displaystyle \mathbb {C} ^{2}} , then every
Abhyankar–Moh_theorem
Theorem in complex analysis
x}{1+x^{2}}}\,dx} , Jordan's lemma here is unnecessary. By definition of the complex line integral, ∫ C R f ( z ) d z = ∫ 0 π g ( R e i θ ) e i a R ( cos θ +
Jordan's_lemma
Transit center in Anaheim, California, United States
Disneyland Resort through Anaheim Resort Transportation ARTIC Sports Complex Line 15. During the 2028 Summer Olympics, the station will serve spectators
Anaheim Regional Transportation Intermodal Center
Anaheim_Regional_Transportation_Intermodal_Center
New York City Subway station in Brooklyn
York City Subway station complex shared by the BMT Fourth Avenue Line, the BMT Brighton Line and the IRT Eastern Parkway Line. Named after Atlantic Avenue
Atlantic Avenue–Barclays Center station
Atlantic_Avenue–Barclays_Center_station
Mumbai Metro's Aqua Line terminal metro station
District Collector, Mumbai Suburban The Bandra Kurla Complex metro station, as part of Mumbai Metro Aqua Line 3, has had a significant impact on the surrounding
Bandra Kurla Complex metro station
Bandra_Kurla_Complex_metro_station
New York City Subway station in Manhattan
both ends. The Times Square–42nd Street complex, including the Eighth Avenue Line, is the busiest station complex in the system, serving 65,020,294 passengers
Times Square–42nd Street station
Times_Square–42nd_Street_station
Street in Montreal, Canada
Montreal. A series of interconnected office tower basements and shopping complexes line the street, parallel to the largest segments of Montreal's underground
Saint_Catherine_Street
New York City Subway station in Manhattan
station complex in the Greenwich Village and Chelsea neighborhoods of Manhattan, on the IRT Broadway–Seventh Avenue Line, the BMT Canarsie Line and the
14th Street/Sixth Avenue station
14th_Street/Sixth_Avenue_station
Neighbourhood in Mumbai Suburban, Maharashtra, India
previously a marshland. It is also the starting point of Line 6 of the city's metro system. Lokhandwala Complex featured in the news headlines when, on 16 November
Lokhandwala_Complex
Imperial complex of religious buildings in Beijing, China
pinyin: Tiāntán) is a complex of imperial religious Confucian buildings situated in the southeastern part of central Beijing. The complex was visited by the
Temple_of_Heaven
New York City Subway station in Manhattan
Subway station complex in Lower Manhattan. It consists of four linked stations on the IND Eighth Avenue Line, the IRT Lexington Avenue Line, the BMT Nassau
Fulton Street station (New York City Subway)
Fulton_Street_station_(New_York_City_Subway)
Abstract simplicial complex describing a graph's cliques
Clique complexes, independence complexes, flag complexes, Whitney complexes and conformal hypergraphs are closely related mathematical objects in graph
Clique_complex
Rapid transit system in Mumbai, India
Kurla Complex to Mankhurd lines. The Andheri-Dahisar line will have connectivity with the existing Line 1 and the proposed JVLR-Kanjurmarg line. All four
Mumbai_Metro
Property of objects which are scaled or mirrored versions of each other
explained in its article, is a misnomer. This is actually the 1-dimensional complex line. Henderson, David W.; Taimiņa, Daina (2005). Experiencing Geometry/Euclidean
Similarity_(geometry)
Computer output device that draws lines on paper by moving a pen
rather than raster graphics as with other printers. Pen plotters can draw complex line art, including text, but do so slowly because of the mechanical movement
Plotter
Theorem on holomorphic functions
holomorphic function cannot map an open disk onto a portion of any line embedded in the complex plane. Images of holomorphic functions can be of real dimension
Open mapping theorem (complex analysis)
Open_mapping_theorem_(complex_analysis)
Metro line in Mumbai, India
Lokhandwala Complex with Vikhroli and will have 13 stations. Pink Line will also provide interchanges with Yellow Line 2 at Adarsh Nagar, with Aqua Line 3 at
Pink_Line_(Mumbai_Metro)
Special tangential structure
equivalently a complex line bundle. Every spin structure induces a canonical spinc structure. The reverse implication doesn't hold as the complex projective
Spinc_structure
Ordinary in heraldic blazon; horizontal band at the top of a coat of arms
point that is one quarter to one third the way down the shield. It is a complex line division variant of a chief. A chief enarched is drawn with a concave
Chief_(heraldry)
Railway station in Norwood, Massachusetts, US
service became the Franklin Line of the MBTA Commuter Rail system. The first part of the 676-unit Windsor Gardens apartment complex opened in 1962. After several
Windsor_Gardens_station
Metro line in Mumbai, India
The line offers interchange with: the Yellow Line at Dahisar (East) the Pink Line at Jogeshwari (East) the Blue Line at Gundavali the Aqua Line at Chhatrapati
Red_Line_(Mumbai_Metro)
New York City Subway station in Brooklyn
New York City Subway station complex shared by the elevated IND Culver Line and the underground BMT Fourth Avenue Line. It is located at the intersection
Fourth Avenue/Ninth Street station
Fourth_Avenue/Ninth_Street_station
Coordination complex of a metal and cyclopentadienyl groups
is typically drawn as a single line from the metal center to the center of the Cp ring. Biscyclopentadienyl complexes are called metallocenes. A famous
Cyclopentadienyl_complex
Rational function of the form (az + b)/(cz + d)
straight line to a line or circle, and map every circle to a line or circle. The Möbius transformations are the projective transformations of the complex projective
Möbius_transformation
Differential map between manifolds whose differential is everywhere surjective
C , C 2 {\displaystyle \mathbb {C} ,\mathbb {C} ^{2}} of the complex line and the complex plane. Note that we should actually remove the points t = 0
Submersion_(mathematics)
New York City Subway station in Manhattan
New York City Subway station complex shared by the BMT Broadway Line, the BMT Canarsie Line and the IRT Lexington Avenue Line. It is located at the intersection
14th Street–Union Square station
14th_Street–Union_Square_station
{\displaystyle \mathbb {C} } -convex if its intersection with any complex line is contractible. In complex geometry and analysis, the notion of convexity and its
Complex_convexity
Station of the Seoul Metropolitan Subway
Sports Complex station is a station on Seoul Subway Line 2 and Seoul Subway Line 9. As its name indicates, it serves the nearby Seoul Sports Complex including
Sports Complex station (Seoul)
Sports_Complex_station_(Seoul)
Disused railway station in Dorset, England
the Easton and Church Hope Railway, one of the constituent parts of a complex line, on 16 October 1865. The station was moved to a new site on the opening
Portland railway station (England)
Portland_railway_station_(England)
Part of a line that is bounded by two distinct end points; line with two endpoints
a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the line that
Line_segment
Software interface based on commands formatted as lines of text
command-line interface (CLI), also known as a command-line shell, is a means of interacting with software via commands – each formatted as a line of text
Command-line_interface
Graphical symbol or pictogram used to point or indicate direction
triangle, chevron, or concave kite, usually affixed to a line segment or rectangle, and in more complex forms a representation of an actual arrow (e.g., ➵ U+27B5)
Arrow_(symbol)
Disused railway station in Dorset, England
a complex line, on 1 September 1902. The line past Portland station was technically a separate railway, although the branch was operated as one line throughout
Easton railway station (England)
Easton_railway_station_(England)
Theorem in complex analysis
In complex analysis, a branch of mathematics, the Hadamard three-line theorem is a result about the behaviour of holomorphic functions defined in regions
Hadamard_three-lines_theorem
Psychological defense mechanism articulated by Alfred Adler
A superiority complex is a defense mechanism that develops over time to help a person cope with feelings of inferiority. The term was coined by Alfred
Superiority_complex
New York City Subway station in the Bronx
is a New York City Subway station complex shared by the IRT Jerome Avenue Line and the IRT White Plains Road Line. It is located at East 149th Street
149th Street–Grand Concourse station
149th_Street–Grand_Concourse_station
Complex exponential in terms of sine and cosine
mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function
Euler's_formula
Section of the field on an escutcheon
an escutcheon Divisions of the field, like the ordinaries, may follow complex line shapes. Most of these "sections" have developed conventional names in
Division_of_the_field
Cooperation between the military and entertainment industries
The military–entertainment complex is the cooperation between militaries and entertainment industries to their mutual benefit, especially in such fields
Military–entertainment complex
Military–entertainment_complex
a complex valued function whose restriction to every complex line is a harmonic function with respect to the real and imaginary part of the complex line
Pluriharmonic_function
New York City Subway station in Queens
station is a New York City Subway station complex served by the IRT Flushing Line and the IND Queens Boulevard Line. Located at the triangle of 74th Street
Jackson Heights–Roosevelt Avenue/74th Street station
Jackson_Heights–Roosevelt_Avenue/74th_Street_station
Opening move sequence for a game of Go
6 may be not only playable, but preferable. The onadare is the most complex line of all: the konadare can lead to a running fight, but tends normally
Nadare_jōseki
Upper-half plane model of hyperbolic non-Euclidean geometry
description of the geodesic flow on the unit-length tangent bundle (complex line bundle) on the upper half-plane. Starting with this model, one can obtain
Poincaré_half-plane_model
Set of topological invariants
deleted). The same construction for complex vector bundles shows that the Chern class defines a bijection between complex line bundles over X and H2(X; Z), because
Stiefel–Whitney_class
Mathematical concept
sizes. For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number
Infinity
Train station in South Korea
Digital Complex Station (Korean: 구로디지털단지역) is a station on the Seoul Subway Line 2. This station will also become a station on the Sin Ansan Line in the
Guro_Digital_Complex_station
Spacetime with complexified coordinates
gravitation and electromagnetism within a complex 4-dimensional Riemannian geometry. The line element ds2 is complex-valued, so that the real part corresponds
Complex_spacetime
Sports and recreational park in Bacolod, Philippines
building inaugurated within the park in 2018. The 25-hectare Panaad Sports Complex, lined with eucalyptus trees and the 32 attractive pavilions for each local
Panaad Park and Sports Complex
Panaad_Park_and_Sports_Complex
Defensive lines of the war
Ukrainians swiftly advanced into adjacent territory. The Surovikin line is a complex set of fortifications in southern and eastern Ukraine, engineered
Fortifications of the Russian invasion of Ukraine
Fortifications_of_the_Russian_invasion_of_Ukraine
Concept in geometry including line and circle
generalised circle, sometimes called a cline or circline, is a straight line or a circle, the curves of constant curvature in the Euclidean plane. The
Generalised_circle
Multipurpose building complex in Chengdu, Sichuan, China
spread over 6 by 8 story blocks around the edge of the complex. The center is connected to Line 1 of the Chengdu Metro. The building will eventually face
New_Century_Global_Center
British shipping company (1845–1934)
Company. Despite this complex organization, the shipping company was known publicly throughout its existence as the White Star Line. A debate reigned as
White_Star_Line
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
of the tangent bundle of X. Significant special cases are when E is a complex line bundle, and when X is an algebraic surface (Noether's formula). Weil's
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
Line formed by the real numbers
continuum. The real line can be embedded in the complex plane, used as a two-dimensional geometric representation of the complex numbers. The first mention
Number_line
COMPLEX LINE
COMPLEX LINE
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Complete
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Tamil
Complete
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Girl/Female
Hindu, Indian
Complex
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Boy/Male
Indian
Complete
Girl/Female
Bengali, Indian
Good Complex
Boy/Male
Tamil
Complete
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Complete
Boy/Male
Indian
Complete
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
COMPLEX LINE
COMPLEX LINE
Girl/Female
Indian, Sanskrit
One that Delights
Boy/Male
Tamil
Manwendra | மாநவேநà¯à®¤à¯à®°Â Â
King among men
Boy/Male
Australian, British, Dutch, English, German, Hebrew
The Lord is Gracious
Boy/Male
Australian, Irish
Guardian
Boy/Male
Muslim/Islamic
Sublime high
Surname or Lastname
English
English : metathesized form of the occupational name Coyner.English : possibly an occupational name for a dealer in rabbits or rabbit skins, from an agent derivative of Middle English cony ‘rabbit’ (see Coney).
Girl/Female
Arabic, Muslim
Olive
Girl/Female
Muslim
Bird of paradise, Auspicious bird, Phoenix
Male
Arthurian
, a giant (alder river).
Girl/Female
Australian, Indian
Name of a God
COMPLEX LINE
COMPLEX LINE
COMPLEX LINE
COMPLEX LINE
COMPLEX LINE
imp. & p. p.
of Comply
a.
Not complex; uncompounded; simple.
n.
One who compiles; esp., one who makes books by compilation.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
a.
Complex, complicated.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
Intricate; entangled; complicated; complex.
a.
Repeatedly compound; made up of complex constituents.
pl.
of Couple-close
a.
One of the pairs of plates of two metals which compose a voltaic battery; -- called a voltaic couple or galvanic couple.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
Two taken together; a pair or couple; especially two lines of verse that rhyme with each other.
a.
See Couple-close.
adv.
In a complex manner; not simply.
a.
That which joins or links two things together; a bond or tie; a coupler.
n.
A complex; an aggregate of parts; a complication.
imp. & p. p.
of Couple
imp. & p. p.
of Compile
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.