Split-complex number

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In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1 {\displaystyle j^{2}=1} , where j ≠ ± 1 {\displaystyle j\neq \pm 1} . A split-complex number has two real number components x and y, and is written z = x + y j . {\displaystyle z=x+yj.} The conjugate of z is z ∗ = x − y j . {\displaystyle z^{*}=x-yj.} Since j 2 = 1 , {\displaystyle j^{2}=1,} the product of a number...

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