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.

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

    “Man cannot bury his meanings so deep in his book, but time and like-minded men will find them. Plato had a secret doctrine, had he? What secret can he conceal from the eyes of Bacon? of Montaigne? of Kant? Therefore, Aristotle said of his works, “They are published and not published.””
    —Ralph Waldo Emerson (1803–1882)

    “All propaganda or popularization involves a putting of the complex into the simple, but such a move is instantly deconstructive. For if the complex can be put into the simple, then it cannot be as complex as it seemed in the first place; and if the simple can be an adequate medium of such complexity, then it cannot after all be as simple as all that.”
    —Terry Eagleton (b. 1943)

    “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)