Definition:Conjugate


 * Group theory: The conjugate of an element or subset $$X$$ of a group $$G$$ by a given element $$a$$ is defined as $$a X a^{-1}$$.
 * 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 $$a \mathbf 1 - b \mathbf i - c \mathbf j - d \mathbf k$$.
 * Geometry: The conjugate of an angle $$\theta$$ is the angle $$2 \pi - \theta$$, that is, the angle that makes a full angle with it.