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    Complex Plane

    Alternate name

    Gauss plane

    Basic definition

    The complex plane is a term for the set of all complex numbers. Just as all real numbers can be imagined as lying on a line, all complex numbers can be thought of as points in a plane.

    Detailed definition

    The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the complex plane. The line in the plane with i = 0 is the real line. The complex plane is sometimes called the Argand plane or Gauss plane, and a plot of complex numbers in the plane is sometimes called an Argand diagram. The complex plane together with the point at infinity C union {∞} is known as the Riemann sphere or extended complex plane and denoted C^* or C^^. However, the notation C^* is also used to denote the punctured plane C - {0}.

    Related terms

    affine complex plane | Argand diagram | Bergman space | Cartesian plane | complex projective plane | C^* | Euclidean plane | extended complex plane | imaginary axis | isotropic line | left half-plane | lower half-disk | lower half-plane | punctured plane | real line | right half-plane | upper half-disk | upper half-plane

    Educational grade level

    high school level (California Algebra II standard)

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