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From: nbp@SWORD.BELLCORE.COM (Nikolaos-John Pronios)
Newsgroups: bit.listserv.hellas
Subject: re: Quiz
Message-ID: <9002110354.AA13978@sword.bellcore.com>
Date: 11 Feb 90 03:54:56 GMT
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	APOPSTOLI:

Quiz:  1=sqrt(1)=sqrt((-1)(-1))=sqrt(-1)*sqrt(-1)=i*i=-1====> 1=-1

APANTHSH:

1=exp(j2pi+2kpi) k integer (2k even)

sqrt(1)=exp(jpi+kpi), k integer, even or odd
			Gia non-complex pairnoume k even (zygo) esti wste k=2l,
			2lpi=> plhrhs peristrofh, pali stous pragmatikous.
			H ypo0esh (assumption) einai oti douleuoume se grammh
			kai oxi se epipedo.

			An einai ka0aro oti douleueis se migadikous,
			0a prepri na pareis oles tis lyseis (k=-inf, 0, inf  akeraios)
			oxi mono tous zygous (even).

-1=exp(jpi+2kpi) k integer odd or even

(-1)(-1)=exp(j2pi+2lpi)=1,  l integer, akomh douleueis ston aksona twn
 pragmatikwn.

sqrt(-1)sqrt(-1)=exp(jpi/2+kpi) exp(jpi/2+kpi)  k integer (vale k1, k2 an
 0eleis)

			Se auto to shmeio, douleueis sto epipedo kai oxi se grammh (eu0eia)
							--------------------------

exp(jpi/2+kpi) exp(jpi/2+kpi) = i * i   Edw agnoeis ta -i pou pairneis gia
 k=odd,
					pairneis mono k=even, pou keintai ston aksona
					twn fantastikwn.


	Etsi auto pou ginetai einai oti eksiswneis ena apo
	ta dyo apotelesmata pou einai dynata
	an douleueis sto complex plane,
	me apotelesma pou pairneis
	an douleueis ston aksona twn pragmatikwn.

En pasei periptwsei,

1=sqrt(1)=sqrt((-1)(-1))=sqrt(-1)*sqrt(-1)=i*i=-1====> 1=-1
					 ^^^
			Ypo0etwntas oti	eixes ksekinhsei
			me migadikous,	edw einai to la0os.
				H isothta den isxyei.

		       ^^^^
		0a mporousa na to valw
		kai edw, mia kai edw
		ginetai h metavash
		apo pragmatiko se migadiko.




	AN synexizes kanonika,

exp(jpi/2+kpi) exp(jpi/2+lpi) =exp(jpi+(k+l)pi)

				kai gia k+l=odd  pairneis  1
			            gia k+l=even pairneis -1



	Auta, elpizw na mhn sas kourasa,


	Nikos P.