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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
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)
Set of lines described by homogeneous polynomial equations
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
{\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
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
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
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
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
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
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
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)
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
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
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
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)
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
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
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
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)
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
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)
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
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
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
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)
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)
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)
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
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
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
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
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)
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
Branch of mathematics
{\displaystyle f(z)=z^{2}} from the complex numbers C to itself. It is helpful to view this as a map from the complex projective line C P 1 {\displaystyle \mathbf
Complex_dynamics
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
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)
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)
Guangzhou Metro interchange station
on Line 3 through this station is very complex. Line 3 branches immediately north of the station, with a branch to Airport North (referred to as Line 3
Tiyu_Xilu_station
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
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
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)
Railway line in North Korea
adjoining Taean Line moves via the P'yŏngnam Line. Steel arrives there from the Kimchaek Iron & Steel Complex, the Hwanghae Iron & Steel Complex and the Ch'ŏllima
Pyongnam_Line
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
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
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
New York City Subway station in Brooklyn
station complex in Brooklyn shared by the BMT Fourth Avenue Line, the IRT Broadway–Seventh Avenue Line and the IRT Eastern Parkway Line. The complex comprises
Borough Hall/Court Street station
Borough_Hall/Court_Street_station
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
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
Upcoming Namma Metro station under Blue Line
DRDO Sports Complex (formerly called as DRDO Sports Complex) is an upcoming elevated metro station on the north-south corridor of the Blue Line of Namma
DRDO Sports Complex metro station
DRDO_Sports_Complex_metro_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
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
In mathematics, a cubical complex (also called cubical set and Cartesian complex) is a set composed of points, line segments, squares, cubes, and their
Cubical_complex
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
New York City Subway station in Brooklyn
station complex shared by the BMT Canarsie Line and the IND Crosstown Line. Located in the Williamsburg neighborhood of Brooklyn, the complex is served
Metropolitan Avenue/Lorimer Street station
Metropolitan_Avenue/Lorimer_Street_station
Stand Alone Complex (攻殻機動隊 STAND ALONE COMPLEX, Kōkaku Kidōtai: Sutando Arōn Konpurekkusu; "Mobile Armoured Riot Police: Stand Alone Complex") is a Japanese
List of Ghost in the Shell: Stand Alone Complex episodes
List_of_Ghost_in_the_Shell:_Stand_Alone_Complex_episodes
COMPLEX LINE
COMPLEX LINE
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Tamil
Complete
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Boy/Male
Tamil
Complete
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
Tamil
Complete
Boy/Male
Indian
Complete
Boy/Male
Indian
Complete
Boy/Male
Tamil
Complete
Girl/Female
Hindu, Indian
Complex
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.
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
Tamil
Complete
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Girl/Female
Bengali, Indian
Good Complex
Girl/Female
Tamil
Complete
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
COMPLEX LINE
COMPLEX LINE
Boy/Male
Tamil
Shamanth | ஷாமாஂதÂ
Universal, Whole, Lord Rama
Girl/Female
Egyptian
Well born.
Boy/Male
Hindu
One who brings good things
Boy/Male
Indian
th Persian month
Boy/Male
Indian, Sikh
Boss; Fast at Running
Boy/Male
Arabic, Muslim
Kindness of Husain
Girl/Female
Tamil
Charulekha | சாரà¯à®²à¯‡à®•à®¾
Beautiful picture
Boy/Male
American, British, English
From the Old Cottage
Girl/Female
Hindu
Rich or from hadria, Gem, Goddess Lakshmi, Graceful, Singer
Girl/Female
Tamil
Idol, Mentor, With An ideology
COMPLEX LINE
COMPLEX LINE
COMPLEX LINE
COMPLEX LINE
COMPLEX LINE
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
n.
A complex; an aggregate of parts; a complication.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
One who compiles; esp., one who makes books by compilation.
imp. & p. p.
of Comply
a.
Complex, complicated.
a.
See Couple-close.
n.
Two taken together; a pair or couple; especially two lines of verse that rhyme with each other.
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.
One of the pairs of plates of two metals which compose a voltaic battery; -- called a voltaic couple or galvanic couple.
imp. & p. p.
of Couple
pl.
of Couple-close
imp. & p. p.
of Compile
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.
That which joins or links two things together; a bond or tie; a coupler.
a.
Not complex; uncompounded; simple.
a.
Intricate; entangled; complicated; complex.
a.
Repeatedly compound; made up of complex constituents.
adv.
In a complex manner; not simply.