Sorry, that was the result of a sloppy edit while writing in the browser; it should say "dot(a, a) == 0 with a non-zero" (Consider a = [1, i]).
(Originally I had something like "dot(a, b) == 0 with a and b non-orthogonal" but it's hard to make that objection formal because people commonly define "orthogonal" as "the dot product is zero")