Topics

Complex numbers

The topic is divided into the following subtopics:
  • Complex numbers in algebraic and trigonometric form
  • Powers and roots of complex numbers
  • Quadratic equations with complex roots

Complex numbers in algebraic and trigonometric form

Part I:
  • Imaginary unit
  • Algebraic form of a complex number – addition, subtraction, multiplication, division
  • Complex conjugate of a complex number
  • Geometric representation of complex numbers in gaussian plain
  • Absolute value of a complex number
Part II:
  • Trigonometric form of a complex number
  • Trigonometric form of a complex number – multiplication, division
  • Trigonometric and algebraic form conversion of complex numbers
Part III:
  • Simple equations of two variables with complex coefficients

Powers and roots of complex numbers

Part I:
  • Powers of complex numbers (de Moivre’s theorem)
Part II:
  • Roots of complex numbers - Binomial equations with real coefficients
Part III:
  • Roots of complex numbers - Binomial equations with complex coefficients

Quadratic equations with complex roots

Part I:
  • Quadratic equations with real coefficients
  • Factoring of quadratic trinomial
Part II:
  • Quadratic equations with real coefficients (complex problems)
  • Quadratic equations with real coefficients with parameter
Part III:
  • Quadratic equations with complex coefficients