Complex Numbers: Polar Form

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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: Representation and Properties

Covers the representation of complex numbers and their properties, including Euler's and Moivre's formulas.

Complex Numbers: Operations and Representations

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

Complex Numbers: Polar Form

Covers the polar form of complex numbers, emphasizing the importance of the argument.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Complex Numbers: Definitions and Properties

Covers the definitions and properties of complex numbers, including conjugate and modulus.

Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, complex sequences, convergence, and continuity of functions.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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.