The [[Complex Conjugate|Conjugate]] of a [[Quaternions|Quaternion]] is an [[Operation|operation]] similar to the [[Complex Conjugate]], where all non-[[Real Numbers|real]] [[Axis|axis]] has its [[Scalar]] flipped. $\huge \begin{align} q &= a+bi+cj+dk \\ q^{*} &=a-bi-cj-dk \end{align}$ The conjugate $^{*}$ is [[Distributive Property|distributive]] over addition. Multiplying any quaternion $q$ by its conjugate $q^*$ equals the [[Distance]] of $q$ to the origin $0$. This is also used to define the square of the [[Vector Magnitude|magnitude]] of $q$. $\huge \begin{align} qq^{*} = q^{*}q = |q|^{2} =a^{2}+b^{2}+c^{2}+d^{2} \end{align}$