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What is the conjugate of a multidimensional number?

Study composition algebras.

Understand geometrically the formulas:

• {$N(xy)=N(x)N(y)$}
• {$N(\lambda x)=\lambda^2 N(x)$}
• {$(x,y)=\frac{1}{2}(N(x+y)-N(x)-N(y))$}
• {$\bar{x} = 2(1,x)-x$}

Conjugate is the positive of the chosen dimension and the negative of all other dimensions. So it is based on a chosen dimension (which is not affected by conjugation).