Date: May 12, 2009 12:59 AM
Author: Kayama
Subject: Re: -1 x -1 ?

If we can use the expression -1=e^{i\pi}, we can show 
-1*-1=e^{i\pi}*e^{i\pi}=1 readily:

if we rotate once 1 (the vector 01) by \pi rad around the origin anticlockwise on the complex plane, we obtain
-1. Further likewise if we rotate -1 by \pi rad once more, we can obtain -1*-1=1.

At least I understand -1*-1=1 in this way. 

In that way we can obtain i (imaginary unit), if we rotate 1 by \pi/2 around the origin anticlockwise. 

If we cannnot allow to use the expression -1=e^[i\pi}, I don't understand -1*-1=1 vividly.