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http://en.wikipedia.org/wiki/Complex_number

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Complex numbers

Mathematics did not start with the concept of the complex numbers. It took many years and much discussion to get this far. Roughly speaking over time mathematicians have broadened the definition of number. Opinions differ as to how to treat the complex numbers philosophically.

Many people argued that it was just an imaginary construct to solve the cubic and shouldn't be considered 'real'. This is the origin of the terms imaginary and real. However it was found that a whole new beautiful world of complex numbers opened up if you did allow them. To represent a solution to the equation shown above (i.e., X * X + 1 = 0) mathematicians chose the letter i. Even with all of these extensions of the naturals we are still not finished.

In order to construct the complex numbers we need only one more assumption: Any set of real numbers with an upper bound has a least upper bound. This fills in the real line with all of the irrational numbers that cannot be derived merely from the equations above. It is worth noting that this is an entirely different type of extension. This is because of the cardinality of complex numbers is greater than that of the rationals. Once this is done all polynomial equations can be solved (although this can be done in smaller fields than the complex numbers).

Mathematicians today rarely view the development of the complex numbers in this way (the preferred teaching method does not emphasize this stepwise development) but it demonstrates the tension in mathematics between the rigorous and the creative which is the main power behind much of modern mathematics.

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http://math.fullerton.edu/math...s/HistoryComplexBib_lnk_1.html

Zbog toga što jednačine tipa x^2+1=0 nema rješenja u polju realnih brojeva.
jer kvardatni korijen nikad nemože biti jednak -1, francuski matematičar Ojler (čini mi se 19. vijek) uvodi pojam "imaginarne jedinice" za rješavanje ovog problema.
Imaginarna jedinica (i) ima svojstvo da je njen kvadrat jednak -1.

Proširivanjem skupa realnih brojeva i uvodeći imaginarnu jedinicu stvaren je novi skup - kompleksnih brojeva. Svaki kompleksni broj se sastoji od 2 dijela, realnog (Re) i imaginarnog dijela (Im). E sad malo guglaj o odnosu skupova realnih i kompleksnih brojeva i zakonitostima.

Samo da ti se zahvalim. :)

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Ma ništa zato :-)

Pozdrav

Jel' moze neko da postavi neki link za primenu kompleksnih u geometriji?

Ojler je bio Švajcarac a ne Francuz

Drugo, teško da je on izmislio kompleksne brojeve, jer su za imaginarne brojeve matematičari znali još od kad su uspeli da reše kvadratnu jednačinu (ako ništa drugo, a ono bar znamo da se jadni Cardan mučio sa kompleksnim brojevima u pokušaju da reši kubnu jednačinu, a to se dešavalo sve u prvoj polovini 16. veka, a Euler je rođen početkom 18. veka). Naravno, u vreme "otkrića" kompleksnih brojeva niko "normalan" se ne bi usudio da tako nešto nazove brojevima...

Što se tiče geometrijske interpretacije kompleksnih brojeva, ako se dobro sećam, za to je zaslužan izvesni Argand (Jean Robert Argand).

Pošto je autor teme zadovoljan odgovorom na pitanje koje je postavio, a polako zalazite u offtopic, postavio sam posebnu temu o primeni kompleksinih brojeva u geometriji tako da tamo možete diskutovati o tome (jer smatram da je to dosta važna oblast i da ne treba biti samo onako "usput" pomenuta). Ovu temu zatvaram.