From: utzoo!utcsrgv!roderick Newsgroups: net.math Title: Re: Solution(?) to oldie but goodie Article-I.D.: utcsrgv.1099 Posted: Thu Feb 24 11:28:22 1983 Received: Thu Feb 24 11:46:23 1983 References: pyuxjj.176 The problem is that the definition of i is not i = sqrt(-1), but that i**2 = -1. These are two completely different things, despite the tempting intuitiveness of the former. Any experience with abstract algebra (especially extension fields; C is R extended with a symbol i defined by i**2 = -1) and you will understand why things like this are done. (For one thing, they don't lead to contradictions like the one you gave.) Finally note that square root is defined as a value which squared gives the original number; in the strictest sense, it is not even a function. Rod Glover U of T ..!utzoo!utcsrgv!roderick