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The bachelor's thesis aims to introduce basic complex analysis theory leading to conformal mappings and to show the use of the Joukowski transform. The finite element method is applied for solving various Laplace equations appearing in potential flow theory.

This thesis deals with algebraic equations in the field of complex numbers and teaching of them in high school mathematics. The thesis is a web page, it includes the definition of complex numbers in various forms (form of ordered pair, algebraic, polar and exponential form) and operations with them, as well as conversions between forms. The main part of the thesis includes solving of linear, quadratic, binomial, trinomial, reciprocal and cubic equations in the field of complex numbers. The lecture is enhanced with interactive applets demonstrating given topic. The thesis also includes solved exercises, as well as exercises leading to sets of points satisfying a condition and two overall tests. Web page created within the thesis can be used by high school pupils and teachers. 1

The aim of the paper is to define and explain terms of phasor and phasor diagram for students of secondary education level in the Czech republic. It is providing a link between the theoretical foundation of the terms in the mathematics based textbooks available on the market and its establishement and practical use in the teaching process. The purpose of the thesis is to explain the problematic of phasor and phasor diagram in the elecrtic load with the alternating current power supply, which consists of rezistor (R), inductor (L) and capacitor (C). In the second part of the paper, the problematic of the complex numbers and its use is described. In this part, the solution of series or parallel RLC circuit is found by the use of phasor diagram or complex numbers. The paper is furthermore providing reader with problems with solution, which serve as an example for the teaching purposes. The paper is providing the reader with a combination of the theoretical foundation of phasor and phasor diagram with their practical use and application, in order to enable a coherent and understandable explanation of the terms.

This thesis deals with complex numbers and teaching of them in high school mathematics. The thesis is a web page, it includes the definition of complex numbers in various forms (form of ordered pair, algebraic, polar and exponential form) and operations and also conversions between forms. The lecture is enhanced with interactive applets, which demonstrate given topic. Solved exercises, exercises leading to set of points satisfying a condition and an overall test are also parts of the thesis. Web page created within the thesis can be used by high school students as well as by teachers. 1