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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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mensanator

Posts: 5,039
Registered: 12/6/04
Re: -1 x -1 ?
Posted: May 12, 2009 1:30 AM
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On May 11, 11:59?pm, Kayama <yano...@earth.ocn.ne.jp> wrote:
> 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.

If you call North positive and face South (negative
direction) and then take a step backwards (negative
relative displacement) then you've moved North one
step (positive absolute displacemrnt).

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