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master's thesis
Primjena kompleksnih brojeva u algebri i geometriji
2022. urn:nbn:hr:126:019320
Kovačević, Maja
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Cite this document

Kovačević, M. (2022). Primjena kompleksnih brojeva u algebri i geometriji (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:019320

Kovačević, Maja. "Primjena kompleksnih brojeva u algebri i geometriji." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:019320

Kovačević, Maja. "Primjena kompleksnih brojeva u algebri i geometriji." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:019320

Kovačević, M. (2022). 'Primjena kompleksnih brojeva u algebri i geometriji', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:019320

Kovačević M. Primjena kompleksnih brojeva u algebri i geometriji [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:019320

M. Kovačević, "Primjena kompleksnih brojeva u algebri i geometriji", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:019320

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Metadata
TitlePrimjena kompleksnih brojeva u algebri i geometriji
Title (english)Application of Complex Numbers in Algebra and Geometry
AuthorMaja Kovačević
MentorLjiljana Primorac Gajčić (mentor)
Committee memberIvan Matić (predsjednik povjerenstva)
Committee memberLjiljana Primorac Gajčić (član povjerenstva)
Committee memberLjerka Jukić Matić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Tema ovog rada su kompleksni brojevi i njihova primjena u algebri i geometriji. Na samom početku rada nalazi se kratki povijesni razvoj kompleksnih brojeva te je navedena njihova primjena u različitim područjima znanosti. Potom slijedi kratki pregled teorije kompleksnih brojeva, krenuvši od samog skupa kompleksnih brojeva, prikaza u kompleksnoj ravnini te njegovim različitim zapisima i računskim operacijama koje smo iskoristili u dokazima matematičkih identiteta. U trećem poglavlju na temelju niza primjera pokazali smo da pomoću trigonometrijskog zapisa kompleksnog broja možemo dokazati niz algebarskih identiteta te na taj način istaknuli važnost primjene u algebri. Na samom kraju dokazali smo trigonometrijske identitet za sinus i kosinus višestrukih kutova te opisali geometrijsku interpretaciju množenja kompleksnih brojeva i na taj način na nizu primjera pokazali njihovu primjenu u geometriji.
Abstract (english)
The topics of this work are complex numbers and their application in algebra and geometry. At the very beginning of the work, there is a short historical development of complex numbers and their application in different fields of science is stated. Then follows a short overview of the theory of complex numbers, starting from the set of complex numbers itself, shown in the complex plane and its different notations and calculation operations that we used in the proofs of mathematical identities. In the third chapter, based on a series of examples, we showed that using the trigonometric notation of a complex number, we can prove a series of algebraic identities, and in this way they emphasized the importance of application in algebra. At the very end, we proved the trigonometric identity for the sine and cosine of multiple angles and described the geometric interpretation of the multiplication of complex numbers and in this way showed their application in geometry through a series of examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:019320
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-09-26 07:42:27