Definition:Conjugate


 * Geometry:
 * The conjugate of an angle $\theta$ is the angle $2 \pi - \theta$, that is, the angle that makes a full angle with it.


 * Group theory:
 * The conjugate of an element or subset $X$ of a group $G$ by a given element $a$ is defined as $a X a^{-1}$.


 * Number theory:
 * The conjugate of the quadratic irrational $r + s \sqrt n$ is $r - s \sqrt n$.


 * Complex analysis:
 * The (complex) conjugate of a complex number $a + i b$ is $a - i b$.


 * Quaternions:
 * The conjugate quaternion of a quaternion $a \mathbf 1 + b \mathbf i + c \mathbf j + d \mathbf k$ is $a \mathbf 1 - b \mathbf i - c \mathbf j - d \mathbf k$.