a^2 = 1, first base vector is a regular one b^2 = -1, second base vector is "imaginary" ab = 0, base vectors are orthogonal (a+b)^2 = a^2 + 2ab + b^2 = 1

a^2 = 1, first base vector is a regular one b^2 = -1, second base vector is "imaginary" ab = 0, base vectors are orthogonal (a+b)^2 = a^2 + 2ab + b^2 = 1 + 2\*0 + (-1) = 0 Trick is taken from conformal geometric algebra [1]. [1] https://en.wikipedia.org/wiki/Conformal_geometric_algebra https://en.wikipedia.org/wiki/Conformal_geometric_algebra