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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: -1 x -1 ?
Replies: 29   Last Post: May 13, 2009 9:01 AM

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Kayama

Posts: 1
From: Matsuyama, Japan
Registered: 5/12/09
Re: -1 x -1 ?
Posted: May 12, 2009 12:59 AM
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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.

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