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KOMPLEKSNI BROJEVI . COMPLEX NUMBERS

Uĉenik: TAMARA ŠEKULARAC, VIII razred OŠ „ KaraĊorĊe“, Beograd

Mentor: VESNA RAJŠIĆ, profesor matematike Elektro tehniĉka škola „Nikola Tesla”, Beograd

REZIME

Razvoj nauke uslovljavao je postavljanje i rešavanje mnogobrojnih problema u raznim prirodnim naukama, pa tako je i u

matematici. Tokom vekova javljali su se problemi u geometriji, aritmetici i drugim oblastima matematike od kojih su neki rešeni.
Neki od tih problema, iako su davno postavljeni, još uvek nisu rešeni. Teorijski rezultati pokazali su da postoje matematiĉki
problemi koji ne mogu ni biti rešeni. Sloţenost problema zahtevala je i razvoj matematiĉkih metoda kojima se ti problemi rešavaju.

To je dovelo do proširivanja postojećih i uvodjenje novih pojmova u matematici. Saznanje o brojevima se širilo od skupa prirodnih
preko skupa celih i racionalnih, do skupa realnih brojeva. Pokazalo se da ovi skupovi nisu dovoljni da opišu prouĉavane pojave
tako da je uveden i skup kompleksnih brojeva. Razvojem teorije kompleksnih brojeva omogućeno je rešavanje realnih problema u

raznim oblastima ljudske delatnosti, kako u praktiĉnim tako i u ĉisto teorijskim zadacima. Kompleksni brojevi se primenjuju u
raznim oblastima matematike (u geometriji, analitiĉkoj geometriji, trigonometriji i kombinatorici) i u raznim oblastima istraţivanja
u domenu fizike i elektronike. Ideja o ovom istraţivanju o kompleksnim brojevima potekla je iz ţelje da još jednom ukaţem na

karakteristike kompleksnih brojeva i rešim do sada za mene veoma sloţene i nerešive matemetiĉke probleme. Kljuĉne reĉi:
kompleksni brojevi, kompleksan broj kao ureĊen par, algebarski oblik kompleksnih brojeva, trigonometrijski oblik kompleksnih

brojeva, primena kompleksnih brojeva, razvoj kompleksnih brojeva

Summary

The development of science conditioned positioning and solving numerous problems in the natural sciences as well as in
mathematics. During the centuries, problems emerged in geometry, arithmetic and other areas of mathematics, some of which have

been solved. Some of these problems, although positioned long time ago, haven‟t been solved yet. Theoretical results have shown
that there are certain mathematics problems that can‟t be solved. The complexity of the problem required the development of
mathematical methods to solve those problems. This led to the extension of the existing and the introduction of new concepts in

mathematics. Knowledge about the numbers was spreading from the set of the natural

numbers over the set of the entire and the rational numbers to the set of the real numbers. It was shown that these sets aren‟t

sufficient to describe the studied phenomenon, so the set of complex numbers was introduced. Development of the theory of
complex numbers enabled the solution of real problems in different areas of human activity, in practical as well as in purely

theoretical tasks. Complex numbers have been applied in different areas of mathematics (in the geometry, analytical geometry,
trigonometry and combinatory) and in different areas of research in the field of physics and electronics. The idea of this research of
complex numbers originated from the desire to point out the characteristics of complex numbers once again and to solve

mathematical problems that were until now very complex and unsolvable for me. Key words: complex numbers, complex numbers
as an arranged pair, algebraic form of complex numbers, trigonometric form of complex numbers, the application of complex
numbers, the development of complex numbers.