The conjugate of a quaternion is used for operations such as rotation of a quaternion by another or rotation of a vector by a quaternion. This is especially useful when you are transforming lighting normals or other operations whereby translation is not needed.

The conjugate is very easy to calculate, requiring only that you negate the vector component of the quaternion. Therefore, if you have the quaternion q = [ n, v], where n is a scalar and v is a vector, the conjugate of q (denoted by the symbol ~) would be ~q = [n, — v]. You will learn how to use the conjugate of a quaternion to rotate other quaternions and vectors in the next section.