Complex Plane - Other Meanings of "complex Plane"

Other Meanings of "complex Plane"

The preceding sections of this article deal with the complex plane as the geometric analogue of the complex numbers. Although this usage of the term "complex plane" has a long and mathematically rich history, it is by no means the only mathematical concept that can be characterized as "the complex plane". There are at least three additional possibilities.

  1. 1+1-dimensional Minkowski space, also known as the split-complex plane, is a "complex plane" in the sense that the algebraic split-complex numbers can be separated into two real components that are easily associated with the point (x, y) in the Cartesian plane.
  2. The set of dual numbers over the reals can also be placed into one-to-one correspondence with the points (x, y) of the Cartesian plane, and represent another example of a "complex plane".
  3. The vector space C×C, the Cartesian product of the complex numbers with themselves, is also a "complex plane" in the sense that it is a two-dimensional vector space whose coordinates are complex numbers.

Read more about this topic:  Complex Plane

Famous quotes containing the words meanings, complex and/or plane:

    The first green night of their dreaming, asleep beneath the Tree,/God said, “Let meanings move,” and there was poetry.
    Muriel Rukeyser (1913–1980)

    Young children constantly invent new explanations to account for complex processes. And since their inventions change from week to week, furnishing the “correct” explanation is not quite so important as conveying a willingness to discuss the subject. Become an “askable parent.”
    Ruth Formanek (20th century)

    As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.
    Henry David Thoreau (1817–1862)