Complex numbers

The topic is divided into the following subtopics:

Complex numbers in algebraic and polar form
Powers and roots of complex numbers
Quadratic equations with complex roots

Complex numbers in algebraic and polar 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:

Polar form of a complex number
Polar form of a complex number – multiplication, division
Polar 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