Complex Numbers: Properties and Operations

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Related lectures (40)

Inverse Element for Multiplication Log in to Mediaspace to watch this video

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

Complex Numbers: Trigonometric Formulas Log in to Mediaspace to watch this video

Explores complex numbers, trigonometric functions, De Moivre's formulas, and complex plane representation.

Complex Numbers: Applications and Representations Log in to Mediaspace to watch this video

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 Applications Log in to Mediaspace to watch this video

Covers the properties and operations of complex numbers and their applications.

Complex Analysis: Holomorphic Functions Log in to Mediaspace to watch this video

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

Complex Numbers: Imaginary Part Log in to Mediaspace to watch this video

Demonstrates how to determine the imaginary part of a complex number.

Complex Logarithm: Extension and Polar Form Log in to Mediaspace to watch this video

Covers the extension of the logarithm to complex numbers and explores the relationship with trigonometric functions.

Sequences: Definitions and Examples Log in to Mediaspace to watch this video

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.

Integration Techniques: Fundamental Theorems and Methods Log in to Mediaspace to watch this video

Discusses integration techniques, focusing on integration by parts and substitution methods, with practical examples and theoretical insights.

Complex Numbers: Polar Form and Multiplication Log in to Mediaspace to watch this video

Covers the polar form of complex numbers and its advantages in multiplication.

Complex Analysis: Functions and Their Properties Log in to Mediaspace to watch this video

Covers the fundamentals of complex analysis, focusing on complex functions, their properties, and applications in solving differential equations.

Applications of Residue Theorem in Complex Analysis Log in to Mediaspace to watch this video

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Analytical Geometry: Proof of Exercise 5 Log in to Mediaspace to watch this video

Focuses on the proof of Exercise 5 in Analytical Geometry, emphasizing trigonometry concepts in solving geometric problems.

Finding Absolute Extrema in Multivariable Functions Log in to Mediaspace to watch this video

Covers the conditions for finding absolute extrema in multivariable functions.

Linear Algebra: Matrices Operations Log in to Mediaspace to watch this video

Covers fundamental matrix operations and their applications in solving linear equations.

Transmission Lines: Arbitrary Terminations Log in to Mediaspace to watch this video

Explores the effects of complex impedance on reflected waves and distribution of quantities.

Vector Spaces: Properties and Operations Log in to Mediaspace to watch this video

Explores vector space properties, operations, linear combinations, and subspaces construction.

Stationary Points Analysis Log in to Mediaspace to watch this video

Covers the analysis of stationary points in functions, focusing on optimization methods.

Embeddability Theorem Log in to Mediaspace to watch this video

Covers the l2-embeddability theorem, isometric embeddings, positive semidefinite matrices, and eigenvalues computation.

Extreme Values and Constraints Log in to Mediaspace to watch this video

Explores extreme values, constraints, Riemann's integral interpretation, and volume calculations of parallelipipeds in mathematics.

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