Realni i kompleksni produkt kompleksnih brojeva i primjene u geometriji trokuta

master's thesis

• Author: Maja Sabati
• Mentor: Mario Krnić (mentor)
• Mentor: Mea Bombardelli (mentor)
• Committee member: Mario Krnić (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Iako su stoljećima bili potpuna nepoznanica, kompleksni brojevi danas su u širokoj primjeni u matematici i znanosti općenito. Cilj ovog diplomskog rada je zagrebati ispod površine i otkriti čari kompleksnih brojeva te pokazati kako operacijama nad njima možemo znatno olakšati rješavanje brojnih geometrijskih problema. U tu svrhu uvest ćemo operacije realnog i kompleksnog produkta kompleksnih brojeva te pomoću njih izvesti neke važne i zanimljive koncepte i rezultate iz geometrije, s naglaskom na geometriju trokuta.

Abstract (english)

Although completely unknown for centuries, complex numbers are nowadays widely used in mathematics and science in general. The aim of this thesis is to scratch beneath the surface and to discover the beauty of complex numbers as well as to show how operations with them can make it much easier to solve many geometric problems. For this purpose, we will introduce the operations of the real and complex product of complex numbers and use them to derive some important and interesting concepts and results in geometry, with an emphasis on triangle geometry.

• Keywords: kompleksni brojevi; rješavanje geometrijskih problema; geometrija trokuta
• Keywords (english): complex numbers; solving geometric problems; triangle geometry
• Language: croatian
• URN:NBN: urn:nbn:hr:217:704187
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-02-26 13:05:21