Agenradbo.134
net.math
utzoo!decvax!genradbo!al
Thu May  6 13:59:21 1982
oldie but goodie (sqrt)

The problem with the sqrt problem has nothing to do with dividing by zero
or because complex numbers are being used.  As some others have stated,
the problem is totally because sqrt(x) is a multi-valued function.
We know that sqrt(1) is both 1 and -1.  One could as well prove in the
real number domain:

sqrt(1) = sqrt(1/1) = sqrt(1)/sqrt(1) = (-1)/1   or   1 = -1

Stated this way, of course, the problem is obvious. Paradoxical proofs
must obscure what is really happening to seem paradoxical.  For the
original proof given, remember that sqrt(-1) is both i and -i.