In the page that talks about comparing imaginary numbers (http://www.cut-the-knot.org/do_you_know/complex_compare.shtml) you mention and example where -1<1, you multiply by i, then i again and you get 1<(-1) -but by multiplying by i twice you are forgetting your inequality rules- you must switch the less than sign to be more then: ergo 1>(-1) and the property holds. Be careful.