Syllabus
Motivation for introducing complex numebrs, Cardan formulas
Algebraic, geometrical and exponential form of complex numebrs. Operations with complex numebrs and their geometrical interpretation
Moivre theorem, roots of complex numebrs, equations with real and complex coefficients, geometrical solution of systems of equations
Complex line, its properties and use for solving geometrical problems in a real plane
Mappings
Complex sequences
Annotation
In the course, students learn theoretical issues concerning complex numbers. The course focuses on properties and forms of complex numbers.
Attention is paid to geometrical interpretations and to links to sequences. The aim is to grasp the structure of complex numbers and get acquainted with their applications useful in other subjects and at the secondary school.