Bicomplex quadratic forms

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The quadratic form associated with a real matrix $Q$ and a real vector $\vec{x}$ is $\langle Q \vec{x}, \vec{x} \rangle$.
The quadratic form associated with a real matrix $Q$ and a complex vector $\vec{x}$ is $\langle Q \vec{x}, \vec{x}^* \rangle$.
What is the quadratic form associated with a real matrix $Q$ and a bicomplex vector $\vec{x}$?