E para complexos ? Ha alguma demonstracao GEOMETRICA de quei i^2 = -1 ?
Aqui eu n�o tenho a menor id�ia do que � que voc� espera: i^2 = -1 � o fato mais b�sico sobre i, n�o sei em que contexto faria sentido demonstrar (geometricamente ou de qualquer outra forma) que i^2 = -1.
Professor Nicolau talvez algo possa ser tirado dos quaternions do Hamilton (n�o me aprofundei muito mas quaternions = vetores?) Veja um peda�o da carta de Sir W. R. Hamilton ao seu filho Archibald.
"But on the 16th day of the same month - which happened to be a Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an under-current of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth, the herald (as I foresaw, immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula with the symbols, i, j, k; namely,
i^2 = j^2 = k^2 = ijk = -1 "
Hamilton se explica melhor em uma carta ao matematico John T. Graves, a carta pode ser vista em pdf: http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/QLetter/QLetter.pdf
ou html
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/QLetter/QLetter.html
Acho que disso pode-se tirar algumas informacoes e relacoes entre vetores numeros complexos e geometria, ou estou enganado?
Um abra�o. -- Niski - http://www.linux.ime.usp.br/~niski
"When we ask advice, we are usually looking for an accomplice." Joseph Louis LaGrange
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