We let sqrt{x} mean "square root of x", and we take i to stand for sqrt{-1} as usual. i^2 = sqrt{(i^2)^2} (sqrt{-1})^2 = sqrt{i^4} -1 = sqrt{1} -1 = 1 0 = 2 0 = 1. Most succinct version: -1 = sqrt( (-1)^2 ) -1 = sqrt( 1 ) -1 = 1. % A variant of this is found in {\em The Moscow Puzzles}, though % that's hardly likely to be the first place given.