Conjugate

[Welington Mina]

In mathematics, a conjugate typically refers to a pair of mathematical expressions or quantities that are connected by a specific mathematical operation yet have opposite components. The term conjugate can have different meanings depending on the domain of math:

1. In complex numbers, the conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

2. In algebra, the conjugate of a binomial expression (a b) is its corresponding binomial formed by negating the second term (a - b) or vice versa.

3. In abstract algebra, conjugate elements in a group are elements related through a similarity transformation.

4. In geometry, conjugate diameters of an ellipse or hyperbola are any two diameters such that a tangent line to the curve at the endpoint of one diameter is parallel to the other diameter, and vice versa.

The broader meaning for conjugate includes the idea of forming a complementary or related pair in a particular mathematical situation.

[Dave Paprocki]

united in pairs; yoked together; coupled

[Sonia]

in single pairs; coupled

[AliceAstes]

containing two or more radicals supposed to act the part of a single one

[gusepinax]

agreeing in derivation and radical signification; -- said of words

[Carmellabita]

presenting themselves simultaneously and having reciprocal properties; -- frequently used in pure and applied mathematics with reference to two quantities, points, lines, axes, curves, etc

[DebrahCom]

to unite in marriage; to join

[Quadirdith 0]

to unite in a kind of sexual union, as two or more cells or individuals among the more simple plants and animals

[Becky]

kon′joo-gāt, v.t. (gram.) to give the various inflections or parts of a verb.—adj. joined: connected.—n. a word agreeing in derivation with another word.—adjs. Con′jugated, Conjugā′tional, Con′jugative, conjugate.—ns. Con′jugateness; Con′jugating; Conjugā′tion, the act of joining: union: (gram.) a term applied to a connected view or statement of the inflectional changes of form that a verb undergoes in its various relations: a class of verbs inflected in the same manner.—Conjugate axes, two axes in a conic section, such that each is parallel to the tangent at the extremity of the other; Conjugate foci (see Focus); Conjugate mirrors, two mirrors set face to face so that the rays emitted from the focus of one are first reflected from it to the and thence to its focus; Conjugation of cells, a mode of reproduction in which two apparently similar cells unite, as in Amœba, Diatoms, c. [L. conjugāre, -ātum—con, together, and jugāre—jugum, a yoke.]

[ArthuraCig]

to bring together in pairs: consisting of a single pair. Conjugation: the union of pairs; usually applied to the merging of the male and female elements.