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  2. Complex multiplication - Wikipedia

    en.wikipedia.org/wiki/Complex_multiplication

    In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. [1] Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice.

  3. Complex multiplier - Wikipedia

    en.wikipedia.org/wiki/Complex_multiplier

    The complex multiplier is the multiplier principle in Keynesian economics (formulated by John Maynard Keynes).The simplistic multiplier that is the reciprocal of the marginal propensity to save is a special case used for illustrative purposes only.

  4. 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.

  5. 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.

  6. Function of several complex variables - Wikipedia

    en.wikipedia.org/wiki/Function_of_several...

    In coordinate-free language, any vector space over complex numbers may be thought of as a real vector space of twice as many dimensions, where a complex structure is specified by a linear operator J (such that J 2 = −I) which defines multiplication by the imaginary unit i. Any such space, as a real space, is oriented.

  7. Root of unity - Wikipedia

    en.wikipedia.org/wiki/Root_of_unity

    The n th roots of unity form under multiplication a cyclic group of order n, and in fact these groups comprise all of the finite subgroups of the multiplicative group of the complex number field. A generator for this cyclic group is a primitive n th root of unity.

  8. Hypercomplex number - Wikipedia

    en.wikipedia.org/wiki/Hypercomplex_number

    The complex numbers are the only 2-dimensional hypercomplex algebra that is a field. Split algebras such as the split-complex numbers that include non-real roots of 1 also contain idempotents and zero divisors (+) =, so such algebras cannot be division algebras.

  9. Schönhage–Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Schönhage–Strassen...

    This section has a simplified version of the algorithm, showing how to compute the product of two natural numbers ,, modulo a number of the form +, where = is some fixed number. The integers a , b {\displaystyle a,b} are to be divided into D = 2 k {\displaystyle D=2^{k}} blocks of M {\displaystyle M} bits, so in practical implementations, it is ...