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Reals with an extra square root of +1 adjoined
In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1 {\displaystyle
Split-complex_number
Number with a real and an imaginary part
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
Complex_number
Two geometries based on axioms closely related to those specifying Euclidean geometry
angle in the split-complex plane correspond to angle in Euclidean geometry. Indeed, they each arise in polar decomposition of a complex number z. Hyperbolic
Non-Euclidean_geometry
Square root of a non-positive real number
always hold for the principal branch of the complex square root function. −1 Dual number Split-complex number j is usually used in engineering contexts
Imaginary_number
Mutation of quaternions where unit vectors square to +1
subalgebras isomorphic to the split-complex number plane. Furthermore, just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic
Hyperbolic_quaternion
{\displaystyle j} of the split-complex numbers, and therefore the multicomplex numbers contain a number of copies of the split-complex number plane. With respect
Multicomplex_number
Study of Lie groups, Lie algebras and differential equations
arises through Euler's formula in the complex plane. Other one-parameter groups occur in the split-complex number plane as the unit hyperbola { exp (
Lie_theory
Historic site in Split, Croatia
Latin: Palatium Diocletiani) is an ancient Roman palace and fortress complex in Split, Croatia. It was built at the end of the third century AD by the Roman
Diocletian's_Palace
Mathematical functions of split-complex numbers
arguments and values in the split-complex number plane, much as functions of a complex variable involve ordinary complex numbers. William Kingdon Clifford
Motor_variable
must use the split forms (of maximally indefinite index), as the group SO is compact. Compact Lie algebra Real form Split-complex number Split orthogonal
Split_Lie_algebra
Mathematical abelian group
Klein four-group. In a similar fashion, the group of units of the split-complex number ring, when divided by its identity component, also results in the
Klein_four-group
between the three planar number systems (complex, dual and split-complex numbers) and the three non-Euclidean geometries. The number system that corresponds
Laguerre_transformations
Coordinates used to specify position of a line
z=\left(\tan {\frac {\theta }{2}}\right)(\cosh s+j\sinh s)} is the split-complex number for a line in the Lobachevski plane. Since there are lines ultraparallel
Line_coordinates
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
Complex_conjugate
Mathematical operation on invertible matrices
plane with ϵ 2 = + 1 {\displaystyle \epsilon ^{2}=+1} , that is a split-complex number plane. Only one quarter of this plane is the image of the exponential
Logarithm_of_a_matrix
Four-dimensional number system
In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition, subtraction, multiplication
Quaternion
Quaternion of norm 1 (unit quaternion)
He saw the modelling power of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend
Versor
Map from a Lie algebra to its Lie group
map, that is, exp ( v ) = v {\displaystyle \exp(v)=v} . In the split-complex number plane z = x + y ȷ , ȷ 2 = + 1 , {\displaystyle z=x+y\jmath ,\quad
Exponential_map_(Lie_theory)
Element of a unital algebra over the field of real numbers
2-dimensional unital algebras over the reals: the ordinary complex numbers, the split-complex numbers, and the dual numbers. In particular, every 2-dimensional
Hypercomplex_number
n\times n} complex unitary matrix. spectrum Set of the eigenvalues of a matrix. split-complex number An element of a split-complex plane. split-complex plane
Glossary_of_linear_algebra
Airport in Kaštela, Croatia
Split Saint Jerome Airport (Croatian: Zračna luka Sveti Jeronim Split; IATA: SPU, ICAO: LDSP), also known as Split Airport (Croatian: Zračna luka Split)
Split_Airport
every complex semisimple Lie algebra g has a split real form, which is unique up to isomorphism. It has maximal index among all real forms. The split form
Real_form_(Lie_theory)
Hypercomplex number system
quotations related to Sedenion. Pfister's sixteen-square identity PG(3,2) Split-complex number "Ensembles de nombre" (PDF) (in French). Forum Futura-Science. 6
Sedenion
Linear map that preserves areas
mapping called a Lorentz boost. This insight follows from a study of split-complex number multiplications and the diagonal basis which corresponds to the pair
Squeeze_mapping
Geometric figure
Whereas the unit circle is associated with complex numbers, the unit hyperbola is key to the split-complex number plane consisting of z = x + yj, where j
Unit_hyperbola
City in Croatia
Split (/splɪt/; Croatian: [splît] ) is the second-largest city in Croatia and the principal urban center of Dalmatia, situated on the eastern shore of
Split,_Croatia
American telephone numbering plan
an area code overlay complex is a telephone numbering plan that assigns multiple area codes to the same geographic numbering plan area (NPA). Area code
Overlay_complex
distinct numbering plan areas (NPAs) which are identified by a total of five area codes, with one of the NPAs being configured as an overlay complex with
List_of_Arizona_area_codes
Pharmaceutical compound
tolerated. Its side effects include rash, diarrhea, fatigue, nausea and raw, split fingertips. The safety profile is manageable with no new safety signals
Daraxonrasib
Element of an algebra using quaternions and split-complex numbers
are split-complex numbers and i, j, and k multiply as in the quaternion group. Since each coefficient w, x, y, z spans two real dimensions, the split-biquaternion
Split-biquaternion
Historical emergence of Christianity
Jerusalem and the First Council of Nicaea. Historiography of the split is complicated by a number of factors, including the diverse and syncretic range of religious
Split of Christianity and Judaism
Split_of_Christianity_and_Judaism
British rapper (born 1998)
his first UK number-one single and preceded their collaborative EP, Split Decision (2023). The song also became the longest-running number-one rap song
Central_Cee
Malformation of the central digit(s) of the hand or foot
families linked to each split hand/foot malformation (SHFM) locus, the large number of morphogens involved in limb development, the complex interactions between
Ectrodactyly
Integrated telephone numbering plan of twenty North American countries
nations has since been recognized as a distinct numbering plan area. For this, numbering plan area 809 was split several times, and now comprises the Dominican
North_American_Numbering_Plan
Area codes in southern California, United States
November 14, 1992, in an area code split of 714 and 840 was added to the numbering plan area to form an overlay complex, effective February 23, 2021. While
Area_codes_909_and_840
American model and socialite (born 1988)
son together in October 2012. They split in 2014 when Tyga began a relationship with Kylie Jenner, leading to a number of social media feuds between Blac
Blac_Chyna
Four-dimensional associative algebra over the reals
generates a complex plane with the real line. For split-quaternions there are hyperboloids of hyperbolic and imaginary units that generate split-complex or ordinary
Split-quaternion
Area code for eastern and southern Arkansas, United States
North American Numbering Plan (NANP) for southern, eastern, and most of northern Arkansas. 870 was created on April 14, 1997, in a split from area code
Area_codes_870_and_327
Branch of pure mathematics
number theory, by contrast, relies on complex numbers and techniques from analysis and calculus. Algebraic number theory employs algebraic structures such
Number_theory
Rookie league in Minor League Baseball
The Arizona Complex League (ACL) is a rookie-level Minor League Baseball league that operates in and around Phoenix, Arizona, since 1988. Prior to 2021
Arizona_Complex_League
Method for producing composition algebras
} A complex number whose second component is zero is associated with a real number: the complex number (a, 0) is associated with the real number a. The
Cayley–Dickson_construction
Telephone area code for Seattle, Washington
telephone numbering plan. After reduction to just the Seattle area over the intervening decades, the numbering plan area was converted to an overlay complex in
Area_code_206
Candy manufacturer
it was announced that the Revere complex would be leased to Amazon for use as a distribution center. Banana Split chews Canada Mints Candy Cupboard &
Necco
Area codes for Phoenix, Arizona, United States
services, the numbering plan area (NPA) was reduced twice in five years in the 1990s. In 1995, the state outside metropolitan Phoenix was split off with area
Area_codes_602,_480,_and_623
Telephone area codes in California
service in 1998, when its services area was split from that of area code 209. 357 was added to form an overlay complex in 2025. In 1997, the California-Nevada
Area_codes_559_and_357
proper time rapidity relativistic wave equations relativistic mass split-complex number unit hyperbola world line black holes no-hair theorem Hawking radiation
List of mathematical topics in relativity
List_of_mathematical_topics_in_relativity
American superhero thriller and psychological horror film series
ranked at number four. Quentin Tarantino also included Unbreakable on his list of top 20 films released since 1992. The second film Split originated
Unbreakable_(film_series)
The North American Numbering Plan (NANP) divides the territories of its members into geographic numbering plan areas (NPAs). Each NPA is identified by
List of North American Numbering Plan area codes
List_of_North_American_Numbering_Plan_area_codes
2005 video game
Xbox. TimeSplitters: Future Perfect is the third and final game in the TimeSplitters series, following TimeSplitters (2000) and TimeSplitters 2 (2002)
TimeSplitters:_Future_Perfect
Mental illness with multiple personality states
dispute is between those who believe DID is caused by traumatic stresses that split the mind into multiple identities, each with a separate set of memories
Dissociative identity disorder
Dissociative_identity_disorder
Area codes for Dayton and part of southwestern Ohio, United States
in September 1996, in a split of area code 513. Area code 326 was added to the numbering plan area to form an overlay complex in March 2020. Area code
Area_codes_937_and_326
Compound with a metal center bound to ligands
coordination number. The most common coordination numbers are 2, 4, and especially 6. A hydrated ion is one kind of a complex ion (or simply a complex), a species
Coordination_complex
Area codes for San Diego County, California
North American Numbering Plan (NANP) for most of San Diego County in the U.S. state of California. Area code 619 was created by a split of area code 714
Area_codes_619_and_858
Area codes in the Los Angeles metropolitan area
the North American Numbering Plan (NANP) for the U.S. state of California. They are assigned in an overlay complex to a numbering plan area (NPA) that
Area_codes_213,_323,_and_738
Telephone area codes for southeastern Virginia, United States
1, 1996 in an area code split of area code 804. Area code 948 was established on February 5, 2020 forming an overlay complex with 757. The service area
Area_codes_757_and_948
The city of Split was founded as the Greek colony of Aspálathos (Aσπάλαθος) in the 3rd or 2nd century BC. It became a prominent settlement around 650
History_of_Split
Casino game of chance
one chip straight-up: one chip on 0–3 split, one on 12–15 split, one on 32–35 split and one straight-up on number 26. This type of bet is popular in Germany
Roulette
transformation z ↦ z e − m j {\displaystyle z\mapsto ze^{-mj}} of the split-complex number plane represents the required transformation since e a j ↦ e ( a
Enrique_Loedel_Palumbo
West Germanic language
and V a vowel. The word strengths /strɛŋθs/ is thus close to the most complex syllable possible in English. The consonants that may appear together in
English_language
Experiment methodology
data, and other, more complex phenomena. "A/B testing" is a shorthand for a simple randomized controlled experiment, in which a number of samples (e.g. A
A/B_testing
Branch of elementary mathematics
inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor. The result
Arithmetic
Telephone area code for northeast Florida, United States
code split of area code 305 in 1965. In 2024, the numbering plan received a second area code, 324 , through the creation of an overlay complex to mitigate
Area_codes_904_and_324
British rapper (born 1998)
Cee), was his third and longest-running number-one song and served as lead single for their collaborative EP, Split Decision (2023). This was later followed
Dave_(rapper)
2025 studio album by Dave
to We're All Alone in This Together (2021), his second studio album, and Split Decision (2023), his collaborative EP with Central Cee. It features guest
The_Boy_Who_Played_the_Harp
Proposed constructs pertaining to the vagus nerve
Polyvagal theory views the parasympathetic nervous system as being further split into two distinct branches: a "ventral vagal system" which supports social
Polyvagal_theory
2019 terrorist attack in Nairobi, Kenya, by al-Shabaab
entrance of the complex, and began firing. They threw two grenades at nearby parked cars at the entrance gate, setting them alight, then split into groups
Nairobi DusitD2 complex attack
Nairobi_DusitD2_complex_attack
American media and entertainment company
announced that go90 would shut down. Complex became known early on for its double-sided covers and split format. Complex covers often combined celebrities
Complex_Networks
Area code of Downtown Chicago
of Illinois' dense population, particularly in the north, the state was split between four NPAs, given that each NPA could only accommodate approximately
Area_code_312
Complex numbers with non-negative imaginary part
\mathbb {R} \}.} The term arises from a common visualization of the complex number x + i y {\displaystyle x+iy} as the point ( x , y ) {\displaystyle (x
Upper_half-plane
Crime organization in South Africa
if they were deceased according to the Number. The relationship between gang members and the warders is a complex and an uneasy one. Under the apartheid
Numbers_Gang
2000 film by M. Night Shyamalan
Split, with Willis reprising his role as David Dunn in a cameo role, was released in January 2017. After the financial and critical success of Split,
Unbreakable_(film)
American rapper (born 1999)
Fordham Ram. Retrieved April 26, 2024. Skelton, Eric. "YNW Melly's Split Reality". Complex. Retrieved April 26, 2024. Wikimedia Commons has media related
YNW_Melly
Area codes in New York City
larger overlay complex with area code 917 which comprises all of New York City. Area code 718 was created in the first area code split of New York City's
Area_codes_718,_347,_and_929
Upcoming multi-sport event in Ahmedabad, India
and domestic programming. In September 2025, the Veer Savarkar Sports Complex was opened, at a cost of ₹825 crores. It is 21 acres in size and has six
2030_Commonwealth_Games
Method in numerical analysis
In numerical analysis, the split-step Fourier method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like
Split-step_method
North American telephone area codes near San Antonio, Texas
an overlay complex, activated in 2017 to alleviate exhaustion concerns in 2018. Area code 210 was created on November 1, 1992, in a split from area code
Area_codes_210_and_726
American singer (born 1942)
in the UK where it reached number five and achieved a Silver Record Award for the second time. After the Union Gap split, Puckett released a solo album
Gary_Puckett
Cell division producing haploid gametes
each chromosome. Errors in meiosis resulting in aneuploidy (an abnormal number of chromosomes) are the leading known cause of miscarriage and the most
Meiosis
Area codes for southern and eastern California
codes in the North American Numbering Plan (NANP) for the U.S. state of California. These area codes serve an overlay complex that comprises much of the
Area_codes_760_and_442
Telephone area code for western Washington, United States
long-distance telephone calls in Operator Toll Dialing. In 1957, the numbering plan area was split, with area code 509 implemented for the state east of the Cascade
Area_code_564
American singer (born 1991)
within minutes. In November 2021, multiple sources claimed the couple had split after 6 years of dating. The breakup was confirmed by Carlson in September
Jesse_Rutherford
Provides integral formulas for all derivatives of a holomorphic function
formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on
Cauchy's_integral_formula
Measure with complex values
is a complex number. Formally, a complex measure μ {\displaystyle \mu } on a measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} is a complex-valued
Complex_measure
Numeric value with an unclear meaning
In computer programming, a magic number or file signature is a numeric literal in source code that has a special, particular meaning that is less than
Magic_number_(programming)
Video game series
TimeSplitters is a series of first-person shooter video games developed by Free Radical Design. The games are often considered spiritual successors to
TimeSplitters
American model and media personality (born 1998)
social media personality and model. She has been featured in campaigns by a number of major brands including Stuart Weitzman, Tommy Hilfiger, Michael Kors
Sofia_Richie
Optical device which splits a beam of light in two
the identity, i.e. the beam-splitter transfer matrix is a unitary matrix. Each r and t can be written as a complex number having an amplitude and phase
Beam_splitter
Floodgate system in Louisiana, USA
preventing the Mississippi River from changing course. Completed in 1963, the complex was built by the U.S. Army Corps of Engineers in a side channel of the
Old_River_Control_Structure
American rapper and YouTuber (born 1997)
debut EP, Take Me Serious. It received over 25 million views on YouTube. Complex identified "Givenchy" as a song "Bout to Blow in 2018". On March 17, 2018
DDG_(rapper)
Apartment complex in Sydney, Australia
The Sirius Building is an apartment complex in The Rocks district of Sydney, New South Wales, Australia. Designed for the Housing Commission of New South
Sirius_Building
United States historic place
juniper post corrals and board fences around the ranch complex. There are also historic split rail and willow fences along with modern steel post fences
David_L._Shirk_Ranch
Energy-producing metabolic pathway
An electron transport chain (ETC) is a series of protein complexes and other molecules which transfer electrons from electron donors to electron acceptors
Electron_transport_chain
Concept of complex analysis
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions
Residue_theorem
Area codes in North Carolina, United States
in a split of numbering plan area 704, the original area code serving the entire state. After successive splits in the 1990s, the final numbering plan
Area_codes_919_and_984
Colorado telephone area codes
Colorado would need another area code. An impending number shortage in the late 1980s meant this split could no longer be staved off. On March 5, 1988, southeastern
Area_codes_303,_720,_and_983
Country mainly in West Asia
national, provincial, and local. The local government's duties are commonly split between municipal governments and districts, in which the executive and
Turkey
Number expressed in the base-2 numeral system
1938 with Stibitz at the helm. Their Complex Number Computer, completed 8 January 1940, was able to calculate complex numbers. In a demonstration to the
Binary_number
Telephone area code for southeastern Georgia, United States
exhaustion relief around 2027. An overlay complex with 912 and area code 565 was approved in May 2025. Numbering plan area 912 includes the counties of Appling
Area_code_912
1961 novel by Joseph Heller
especially doctors and military leaders. The development of the novel can be split into sections: The first (chapters 1–11) broadly follows the story fragmented
Catch-22
Property in optics
traveling in the x-direction. This can be done by relating the complex wave number k to the complex refractive index n through k = 2πn/λ0, with λ0 being the
Refractive_index
SPLIT COMPLEX-NUMBER
SPLIT COMPLEX-NUMBER
Boy/Male
Tamil
Inside viewer, Spilt second
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
Momentary; Split Second
Boy/Male
Muslim
Strong, Solid, Firm, Sharp
Girl/Female
American, Christian, Hebrew, Indian
Narrow Split of Land
Boy/Male
Arabic, Muslim, Sindhi
Split
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
Hindu
Inside viewer, Spilt second
Girl/Female
Hindu, Indian, Telugu
Motherly Love; Energetic Sprit
Girl/Female
Bengali, Indian
Good Complex
Boy/Male
Muslim
Split, Cleavage
Boy/Male
Hindu
Inside viewer, Spilt second
Boy/Male
American, British, English
From the Split Meadow
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Boy/Male
Tamil
Inside viewer, Spilt second
Boy/Male
Arabic, Muslim
Strong; Solid; Firm; Sharp
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
Muslim/Islamic
Split Cleavage
Boy/Male
English
From the split meadow.
Girl/Female
Hindu, Indian
Complex
SPLIT COMPLEX-NUMBER
SPLIT COMPLEX-NUMBER
Girl/Female
Tamil
Proudly, King
Girl/Female
Teutonic
Intelligent.
Girl/Female
Sikh
Beautiful
Boy/Male
Anglo Saxon American German English Shakespearean
Guardian.
Boy/Male
Arabic, British, English
Carrier; Bearer; Home-lover's Estate or Hill with Grass
Male
English
Medieval pet form of English Jordan, JUDD means "flowing down."
Boy/Male
Hindu, Indian
Bright; Open Eyed Therefore Attractive
Girl/Female
Indian, Kannada
The Sun
Boy/Male
Arabic, Hindu, Indian, Muslim, Sindhi
Counsels or Brings Together
Girl/Female
American, Australian, British, English, Irish
Pale-skinned; Dark; Black; Pale; White
SPLIT COMPLEX-NUMBER
SPLIT COMPLEX-NUMBER
SPLIT COMPLEX-NUMBER
SPLIT COMPLEX-NUMBER
SPLIT COMPLEX-NUMBER
a.
Intricate; entangled; complicated; complex.
n.
the substitution of more than one share of a corporation's stock for one share. The market price of the stock usually drops in proportion to the increase in outstanding shares of stock. The split may be in any ratio, as a two-for-one split; a three-for-two split.
a.
Not complex; uncompounded; simple.
a.
Complex, complicated.
v. i.
To attend to a spit; to use a spit.
v. t.
A splint bone.
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
v. t.
To divide lengthwise; to separate from end to end, esp. by force; to divide in the direction of the grain layers; to rive; to cleave; as, to split a piece of timber or a board; to split a gem; to split a sheepskin.
imp. & p. p.
of Spit
v. t.
One of the small plates of metal used in making splint armor. See Splint armor, below.
a.
Repeatedly compound; made up of complex constituents.
n.
A piece that is split off, or made thin, by splitting; a splinter; a fragment.
imp. & p. p.
of Split
v. t.
To split into splints, or thin, slender pieces; to splinter; to shiver.
v. i.
To part asunder; to be rent; to burst; as, vessels split by the freezing of water in them.
adv.
In a complex manner; not simply.
v. t.
To divide or separate into components; -- often used with up; as, to split up sugar into alcohol and carbonic acid.
imp. & p. p.
of Slit
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
v. t.
A piece split off; a splinter.