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  2. Complex number - Wikipedia

    en.wikipedia.org/wiki/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 i 2 = −1.

  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. Complex conjugate - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate

    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 sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}

  6. Residue (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Residue_(complex_analysis)

    Suppose a punctured disk D = {z : 0 < |z − c| < R} in the complex plane is given and f is a holomorphic function defined (at least) on D. The residue Res( f , c ) of f at c is the coefficient a −1 of ( z − c ) −1 in the Laurent series expansion of f around c .

  7. Split-complex number - Wikipedia

    en.wikipedia.org/wiki/Split-complex_number

    Olariu, Silviu (2002) Complex Numbers in N Dimensions, Chapter 1: Hyperbolic Complex Numbers in Two Dimensions, pages 1–16, North-Holland Mathematics Studies #190, Elsevier ISBN 0-444-51123-7. Poodiack, Robert D. & Kevin J. LeClair (2009) "Fundamental theorems of algebra for the perplexes", The College Mathematics Journal 40(5):322–35.

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  9. 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) numbers −1, 2, −2, i. The standard binary (which requires a sign, first line) and the "negabinary" systems (second ...