Definition:Conjugate
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Conjugate may refer to:
- Geometry:
- The conjugate of an angle $\theta$ is the angle $2 \pi - \theta$, that is, the angle that makes a full angle with it.
- The conjugate axis of a hyperbola.
- Conjugate points: Points which line on each other's polar with respect to a circle
- Conjugate lines: polars with respect to a circle whose poles lie on each other
- Conjugate diameters in a central conic.
- Group theory:
- The conjugate of an element or subset $X$ of a group $G$ by a given element $a$ is defined as $a X a^{-1}$.
- Generated normal subgroup of a subset of a group, also known as the conjugate closure of such a subset.
- 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 $a \mathbf 1 - b \mathbf i - c \mathbf j - d \mathbf k$.