23 Nov
2007
23 Nov
'07
10:10 p.m.
On Nov 23, 2007 7:25 PM, Kerry Mitchell <lkmitch@gmail.com> wrote:
Ok, I'll show my ignorance here. How can we distinguish between 1 and -1 and not be able to distinguish between i and -i? Isn't the simple fact that they're distinct numbers (or distinct points in the complex plane) enough? What am I missing?
Take any statement involving i and -i and interchange them -- the statement ought to still be true. For instance, 1/i = -i and 1/-i = i. Try the same with -1 and 1, and you'll have lots of trouble: for instance, 1*1 = 1 but -1 * -1 doesn't equal -1. --Joshua Zucker