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The paper presents results of the work of an international group of students in the frames of the realization of the research net project “Mathematical mosaic”. The results are obtained during investigations applying software products GeoGebra, Geometer's Sketchpad and Maple. The method of the complex numbers is used for the proofs of the assertions. [ABSTRACT FROM AUTHOR]

The students learn about complex numbers and Euclidean plane geometry in high school. Nevertheless, this material is separated into units instead of being integrated. (Anevska, 2014) presents methodological aspects about the study of exponential presentation of the complex numbers and (Anevska & al.2015-1) presents the possibility for inter-subject integration of the mathematics instruction in the study of the mentioned topics. Further on, (Anevska & al., 2015-2) and (Anevska & al., 2016) present the results of the comparative analyses of the scores of the students regarding the transformations in the Euclidean plane and the metric characteristics of the geometric figures and their use when studied in the standard way (see (Mitrović & al., 1998)), and when studied with the use of complex numbers (see (Malcheski & al., 2015)). This paper offers analogous analyses regarding the acquired knowledge in these two ways when solving constructive tasks. [ABSTRACT FROM AUTHOR]

The study of Euclidean plane geometry is compulsory for high school students. Practice shows that even the most advanced students face diffi culties when learning this material, and especially the content related to the metric characteristics of the geometric fi gures and their use. On the other hand, the high school syllabus also includes complex numbers, characterized by an analytical apparatus, which is adequate for learning Euclidean plane geometry. This paper presents the results of a comparative analysis of the scores of the students related to the metric characteristics of the geometric fi gures in the Euclidean plane and their use, when studied with the use of complex numbers (Malcheski, Grozdev & Anevska, 2015), and when studied in a standard way (Mitrović & al., 1998). [ABSTRACT FROM AUTHOR]

Adopting transformations in the Euclidean plane and their application is compulsory for high school students. The practice shows that even advanced students face diffi culties when learning such a material, especially the part which refers to group properties. On the other hand, complex numbers are also studied in high school and they are characterized by an analytical apparatus which helps learning the transformations in the Euclidean plane. This paper presents results from a comparative analysis referring to the accomplishments of the students who study transformations in the Euclidean plane and their application by using complex numbers (see (Malcheski et al., 2015)) and in the classical way (see (Mitrović et al., 1998)). [ABSTRACT FROM AUTHOR]