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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
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
{\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
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
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
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
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
{\bigl (}{\tfrac {\theta }{2}}{\bigr )}\ (\cosh s+j\sinh s)} is the split-complex number for a line in the Lobachevski plane. Since there are lines ultraparallel
Line_coordinates
City in Croatia
Split (/splɪt/; Croatian: [splît] ) is the second-largest city in Croatia, after the capital Zagreb, situated on the eastern shore of the Adriatic Sea
Split,_Croatia
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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)
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 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
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
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
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
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
Residential development in Northern Ireland
a hotel, and a number of retail units, split across three buildings. The name "Arc" is an abbreviation for Abercorn Residential Complex, and also refers
The_Arc_apartments
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
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
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
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
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
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
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
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
Numeric value with an unclear meaning
In computer programming, a magic number or magic constant is a numeric literal in source code whose meaning is unclear to the reader. The term is also
Magic_number_(programming)
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
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
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, 929, and 465
Area_codes_718,_347,_929,_and_465
Cooling of air in an enclosed space
kW very large: >14 kW Ductless systems (often mini-split, though there are now ducted mini-split) typically supply conditioned and heated air to a single
Air_conditioning
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
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
1994 studio album by Aaliyah
Age Ain't Nothing but a Number is the debut studio album by American singer Aaliyah. It was released on May 24, 1994, by Blackground Records and Jive Records
Age Ain't Nothing but a Number
Age_Ain't_Nothing_but_a_Number
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)
Mathematical function that preserves angles
conformal map. Each is hosted by its own real algebra, ordinary complex numbers, split-complex numbers, and dual numbers. The conformal maps are described
Conformal_map
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
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
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
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
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
Describes statistically the splitting of primes in a given Galois extension of Q
of degree n {\displaystyle n} , then the prime numbers that completely split in K {\displaystyle K} have density 1 / n {\displaystyle 1/n} among all
Chebotarev_density_theorem
American venture capital firm
the “largest completed this year by a venture firm.” The funds will be split between a $4 billion late-stage investment fund and a $1 billion fund dedicated
Thrive_Capital
American actress (born 1986)
Josh (December 29, 2010). "Emmy Rossum's Low-Budget Divorce: How Much Did Split Cost Her?". E! News. Archived from the original on December 17, 2014. Retrieved
Emmy_Rossum
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
Type of algebras, possibly non associative
a split algebra: binarions: complex numbers with quadratic form x2 + y2 and split-complex numbers with quadratic form x2 − y2, quaternions and split-quaternions
Composition_algebra
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
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
American singer, songwriter, and actress (born 1993)
(October 17, 2018). "Ariana Grande Reveals She's Suffering from Anxiety After 'Split' from Pete Davidson". Daily Mirror. Archived from the original on October
Ariana_Grande
Measure of the structural complexity of a software program
usefulness of McCabe's number has been questioned. The essence of this observation is that larger programs tend to be more complex and to have more defects
Cyclomatic_complexity
Marble mausoleum in Agra, India
Shah Jahan himself. The tomb is the centrepiece of a 17-hectare (42-acre) complex, which includes a mosque and a guest house, and is set in formal gardens
Taj_Mahal
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
Discrete Fourier transform algorithm
a wide range of published theories, from simple complex-number arithmetic to group theory and number theory. The best-known FFT algorithms depend upon
Fast_Fourier_transform
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
Football tournament qualification stage
(local times, if different, are in parentheses). The qualifying phase is split into two paths – the Champions Path and the Main Path. The Champions Path
2026–27 UEFA Europa League qualifying
2026–27_UEFA_Europa_League_qualifying
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
Invariant that plays a role in algebraic geometry and singularity theory
Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f
Milnor_number
American rapper (born 1991)
American rapper, singer, songwriter, and record producer. Scott has had five number-one hits on the U.S. Billboard Hot 100 chart, along with a total of over
Travis_Scott
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
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)
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
American rapper
Complex. September 8, 2025. "Iggy Azalea and Playboi Carti Reportedly Break up". December 18, 2019. "Playboi Carti and Iggy Azalea Reportedly Split"
Playboi_Carti
International football competition
depending on the number of participants. The group winners will be promoted to League A for round 2. Round 2: The teams in League A will be split into seven
2027 UEFA European Under-19 Championship qualification
2027_UEFA_European_Under-19_Championship_qualification
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