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Gaussian Integer

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A Gaussian integer is a complex number a + b i, where a and b are integers and i is the imaginary unit.

Gaussian integer is a college-level concept that would be first encountered in an abstract algebra course covering rings and fields.

Examples

i: i is the symbol used to denote the principal square root of -1, also called the imaginary unit.

Prerequisites

Algebraic Number: An algebraic number is a number that is the root of some polynomial with integer coefficients. Algebraic numbers can be real or complex and need not be rational.
Complex Number: A complex number is a number consisting of a real part and an imaginary part. A complex number is an element of the complex plane.
Field: A field is a ring in which every nonzero element has a multiplicative inverse. The real numbers and the complex numbers are both fields.
Integer: An integer is one of the numbers ..., -2, -1, 0, 1, 2, ....

Classroom Articles on Rings and Fields

  • Algebra
  • Quaternion
  • Finite Field
  • Ring
  • Ideal

  • Classroom Articles on Abstract Algebra (Up to College Level)

  • Abelian Group
  • Group Representation
  • Abstract Algebra
  • Group Theory
  • Boolean Algebra
  • Isomorphism
  • Cyclic Group
  • Normal Subgroup
  • Dihedral Group
  • Simple Group
  • Finite Group
  • Subgroup
  • Group
  • Symmetric Group
  • Group Action
  • Symmetry Group