To change a verb to accord with time or subject (or, in some languages, object) or all three or (in a few more languages, even more conditions which we won't get into here.)

The conjugate of a complex number a + bi is a - bi. There are various ways of denoting this, but the modern standard is, for the number A, A-bar.

The conjugate of a real number is, therefore, itself, hence this isn't often seen. The conjugate of a pure imaginary number is it's own negative - again, fairly useless.

To generalize the first definition to quaternions, the conjugate of a + bi + cj + dk is a - bi - cj - dk. This is frequently encountered in the multiplicate inverse:
a-1 = ~a / (a · ~a)
Where ~a is the conjugate of a.

Paired together.

1. In chemistry, this refers to an acid and a base which can convert to each other by the gain or loss of a proton (a hydrogen nucleus), which together are called a "conjugate acid-base pair." It can also refer to two liquids in equilibrium with each other.
2. In mycology (the study of fungi), this refers to a dikaryon with two haploid nuclei in it.

From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.

Con"ju*gate (?), a. [L. conjugatus, p.p. or conjugare to unite; con- + jugare to join, yoke, marry, jugum yoke; akin to jungere to join. See Join.]

1.

United in pairs; yoked together; coupled.

2. Bot.

In single pairs; coupled.

3. Chem.

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

[R.]

4. Gram.

Agreeing in derivation and radical signification; -- said of words.

5. Math.

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

Conjugate axis of a hyperbola Math., the line through the center of the curve, perpendicular to the line through the two foci. -- Conjugate diameters Conic Sections, two diameters of an ellipse or hyperbola such that each bisects all chords drawn parallel to the other. -- Conjugate focus Opt. See under Focus. -- Conjugate mirrors Optics, two mirrors so placed that rays from the focus of one are received at the focus of the other, especially two concave mirrors so placed that rays proceeding from the principal focus of one and reflected in a parallel beam are received upon the other and brought to the principal focus. -- Conjugate point Geom., an acnode. See Acnode, and Double point. -- Self-conjugate triangle Conic Sections, a triangle each of whose vertices is the pole of the opposite side with reference to a conic.

Con`ju*gate (?), n. [L. conjugatum a combining, etymological relationship.]

1.

A word agreeing in derivation with another word, and therefore generally resembling it in signification.

We have learned, in logic, that conjugates are sometimes in name only, and not in deed. Abp. Bramhall.

2. Chem.

A complex radical supposed to act the part of a single radical.

[R.]

Con"ju*gate (?), v. t. [imp. & p.p. Conjugated; p.pr. & vb.n. Conjugating.]

1.

To unite in marriage; to join.

[Obs.]

Sir H. Wotton.

2. Gram.

To inflect (a verb), or give in order the forms which it assumed in its several voices, moods, tenses, numbers, and persons.

Con"ju*gate, v. i. Biol.

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

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