Questions involving split complex numbers, that is numbers of the form $a+bj$ where $j^2=1,j\ne\pm 1$ and $a,b\in\mathbb{R}$.

Split complex numbers are numbers of the form $a+bj$, for $a$ and $b$ real numbers. Split complex numbers can also be written in the form of $e^{j\theta}=\cosh\theta+j\sinh\theta$.

For $z=a+bj,\bar z=a-bj$ we have $z\times \bar z=(a+bj)(a-bj)=a^2-b^2$ and so split complex numbers are also sometimes called hyperbolic numbers.

See also: quadratic-forms