The Proofs of Geometrical Statements by Means of Complex Numbers

U ovom radu su dani dokazi nekih vrlo poznatih teorema iz geometrije korištenjem kompleksnih brojeva. Najprije su sustavno razmatrani osnovni pojmovi i relacije vezane uz kompleksne broje koje se koriste u dokazima tvrdnji. Izvedene su jednadžbe geometrijskih figura koje se spominju u tvrdnjama. Primjenom kompleksnih brojeva dokazani su Eulerov, Feuerbachov, Morleyev, Ptolomej-Eulerov, Simsonov te Napoleonov i van Aubelov teorem.This paper will give proofs of some very well-known geometry theorems by using complex numbers. Firstly, we will contemplate some basic concepts and relations related to complex numbers that are used in statement proofs. We will give some equations of geometric figures which are mentioned in these statements. By using complex numbers, we will prove Euler’s, Feuerbach’s, Morley’s, Ptolemy-Euler’s, Simson’s, Napoleon’s and van Aubel’s theorem