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  2. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1. 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 unit and satisfying the equation =; every complex number can be expressed in the form ...

  3. Geometry of Complex Numbers - Wikipedia

    en.wikipedia.org/wiki/Geometry_of_Complex_Numbers

    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 .

  4. cis (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Cis_(mathematics)

    x is the argument of the complex number (angle between line to point and x-axis in polar form). The notation is less commonly used in mathematics than Euler's formula , e ix , which offers an even shorter notation for cos x + i sin x , but cis(x) is widely used as a name for this function in software libraries .

  5. Grassmann number - Wikipedia

    en.wikipedia.org/wiki/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 .

  6. Circle group - Wikipedia

    en.wikipedia.org/wiki/Circle_group

    A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized by the angle measure ⁠ ⁠: = = ⁡ + ⁡. This is the exponential map for the circle group.

  7. Complex-base system - Wikipedia

    en.wikipedia.org/wiki/Complex-base_system

    Binary coding systems of complex numbers, i.e. systems with the digits = {,}, are of practical interest. [9] Listed below are some coding systems , (all are special cases of the systems above) and resp. codes for the (decimal) numbers1, 2, −2, i. The standard binary (which requires a sign, first line) and the "negabinary" systems (second ...

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