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