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Lecture
Complex Numbers: Argument and Polar Method
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Polynomials with Real Coefficients
Explores polynomials with real coefficients, complex roots, and sequences' properties.
Circular Trigonometry: Understanding Geometric Angles
Explores the concept of angles in circular trigonometry, emphasizing geometric angles and their properties.
Sequences: Definitions and Examples
Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.
Square Roots and Complex Numbers
Explores square roots in quadratic equations, complex numbers, Fermat prime numbers, and the Gauss-Wantzel theorem.
Integration of Rational Functions
Covers the integration of rational functions and the decomposition into irreducible factors.
Complex Numbers: Properties and Operations
Explores complex numbers, Euler's formula, Moivre's formula, and proof by induction.
Complex Numbers: Operations and Applications
Explores complex number properties, roots, and polynomial equations in the complex plane.
The Fundamental Theorem of Algebra
Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.
Complex Numbers: Polar Representation
Explores the polar representation of complex numbers and its applications.
Complex Numbers: Polar Form
Explores complex numbers in polar form, Euler's formula, and coordinate transformation.