Introduction to Complex Numbers

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Page 2 of 4

Complex Numbers: Properties and Operations

Explores complex numbers, Euler's formula, Moivre's formula, and proof by induction.

Complex Numbers: Roots and Equations

Explores complex numbers, roots, equations, and polynomial factorization with real coefficients.

Complex Exponential: Properties and Formulas

Delves into complex exponential functions, their properties, and polar representation of complex numbers.

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Euler and Moivre Formulas

Covers Euler and Moivre formulas, addition formulas, properties of exponentials, and generalizing sine and cosine definitions to complex numbers.

Complex Numbers: Polar Representation

Explores the polar representation of complex numbers and its applications.

Inverse Element for Multiplication

Covers the inverse element for multiplication and introduces the Euler and Moivre formulas in complex numbers.

Complex Numbers: Applications and Representations

Explores the origin, applications, and representations of complex numbers in crystallography and materials science, including their graphical, polar, and exponential forms.

Complex Numbers: Operations and Representations

Covers the operations and representations of complex numbers, including the Cartesian and polar forms.

Complex Numbers: Algebraic Structure

Explores the algebraic structure and properties of complex numbers, including Euler's and Moivre's formulas.