conjugué

Conjugue is a term with different meanings depending on the context, primarily in grammar and mathematics.

In grammar, a conjugated verb is a verb that has been modified to indicate a particular tense, mood, person, or number. For example, in English, the verb "to walk" can be conjugated into "walks" (third person singular present), "walked" (past tense), or "walking" (present participle). This process of changing a verb's form is called conjugation. Different languages have complex and varied conjugation systems, often involving specific endings or internal vowel changes to convey grammatical information.

In mathematics, the term "conjugate" typically refers to a related complex number. For a complex number in the form a + bi, where 'a' is the real part and 'b' is the imaginary part, its complex conjugate is a - bi. The real parts are the same, while the imaginary parts have opposite signs. The conjugate of a complex number is often denoted by a bar over the number or an asterisk. For example, the conjugate of z = 3 + 4i is denoted as z̄ or z* and is equal to 3 - 4i. Conjugates are important in various mathematical operations, such as simplifying expressions involving complex numbers and solving certain types of equations. The concept of conjugate also appears in other mathematical areas, like quadratic irrationals, where the conjugate of a + √b is a - √b.