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  2. Grassmann number - Wikipedia

    en.wikipedia.org/wiki/Grassmann_number

    Grassmann number. In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber ), is an element of the exterior algebra of a complex vector space. [ 1] The special case of a 1-dimensional algebra is known as a dual number. Grassmann numbers saw an early use in physics to express ...

  3. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    Complex number. A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system ...

  4. Bicomplex number - Wikipedia

    en.wikipedia.org/wiki/Bicomplex_number

    Bicomplex number. In abstract algebra, a bicomplex number is a pair (w, z) of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate , and the product of two bicomplex numbers as. Then the bicomplex norm is given by. a quadratic form in the first component.

  5. Hypercomplex number - Wikipedia

    en.wikipedia.org/wiki/Hypercomplex_number

    Hypercomplex number. In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.

  6. Geometry of Complex Numbers - Wikipedia

    en.wikipedia.org/wiki/Geometry_of_Complex_Numbers

    1979 edition. Geometry of Complex Numbers is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean geometry. It was written by Hans Schwerdtfeger, and originally published in 1962 as Volume 13 of the Mathematical Expositions series of the University of Toronto Press.

  7. Multicomplex number - Wikipedia

    en.wikipedia.org/wiki/Multicomplex_number

    Multicomplex number. In mathematics, the multicomplex number systems are defined inductively as follows: Let C 0 be the real number system. For every n > 0 let in be a square root of −1, that is, an imaginary unit. Then . In the multicomplex number systems one also requires that ( commutativity ). Then is the complex number system, is the ...

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