 In particular, if , then
This allows the definition of the conjugate of "Â" as
or, 

The product of a dual quaternion with its conjugate yields
This is a dual scalar which is the "magnitude squared" of the dual quaternion.A second type of conjugate of a dual quaternion is given by taking the dual number conjugate, given by

The quaternion and dual number conjugates can be combined into a third form of conjugate given by

In the context of dual quaternions, the term "conjugate" can be used to mean the quaternion conjugate, dual number conjugate, or both.The "norm" of a dual quaternion is computed using the conjugate to compute .