The True Algebra of Complex Numbers - Via Dihedrons
Exploring complex numbers through Dihedron algebra, offering a fresh perspective on their structure and geometry. Highlights include quadratic inverse algebras and comparisons to Quaternions.
The Remarkable Dihedron Algebra - Famous Math Problems
Explore the Dihedron algebra, a key to constructing complex numbers. Learn its basis, properties, and connections to group theory in this comprehensive mathematical exploration.
How to Construct the True Complex Numbers I - Famous Math Problems
Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.
The Projective Line, Circles and a Proof of the CQQ Theorem - Rational Geometry Math Foundations
Explore projective parametrization of the unit circle, derive formulas for areas of triangles and quadrilaterals, and delve into circle geometry with applications to other conics.
The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems
Explore complex numbers and their connection to plane rotations, laying the groundwork for understanding quaternions and 3D rotations. Emphasizes a logical, algebraic approach without relying on transcendental functions.
The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems
Explore quaternions and their connection to 3D rotations using 2x2 complex matrices. Learn key formulas and visual models for this algebraic structure without relying on transcendental concepts.
Complex Numbers and Algebra - Math History - NJ Wildberger
Explore complex numbers' history, applications in cubic equations, and geometric representations. Delve into the Fundamental Theorem of Algebra and its proofs by d'Alembert and Gauss.
Complex Analysis - Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates
Introduction to complex numbers, their arithmetic operations, Euler's formula, and polar coordinates. Covers solutions to differential equations and lays foundation for further complex analysis topics.
Complex Numbers and Functions
Explore complex numbers, Euler's formula, and functions of Z in engineering mathematics, covering geometric interpretations and convergent Taylor series.
Problem Solving - Complex Number Basics
Explore essential complex number techniques for problem-solving contests, covering arithmetic operations, Euler's formula, and nth roots of unity with practical examples.
Homological Mirror Symmetry - Maxim Kontsevich Pt. III
Explore advanced algebraic concepts with Maxim Kontsevich, focusing on Getzler-Gauss-Manin connections for non-commutative algebras and their applications in quantum mathematics.
The Number `E' by Tanvi Jain
Explore the mathematical constant 'e', its history, applications in compound interest, logarithms, calculus, and complex numbers. Discover its irrationality and significance in various mathematical contexts.
Numerical Computation of Monodromy Action Over R
Explore numerical computation of monodromy action over real numbers, focusing on a new piece-wise approach for analyzing real solution sets, with applications in kinematics and mechanism calibration.
Intermediate Algebra - An Introduction to Operations with Complex Numbers
Explore operations with complex numbers, including addition, subtraction, multiplication, and division, enhancing your understanding of advanced algebraic concepts.
Finding All Solutions of Polynomials
Learn to fully factor polynomials over complex numbers and find all solutions, including complex ones, in this comprehensive algebra lesson.
Advanced Engineering Mathematics
Comprehensive exploration of advanced mathematical concepts, including complex analysis, transforms, probability, linear algebra, and more, with applications to engineering problems.
A Level P3 Complex Number
Master complex numbers and polynomials for A Level P3 with comprehensive practice sessions covering key concepts and problem-solving techniques.
What Are Complex Numbers - Essence of Complex Analysis
Comprehensive guide to complex numbers, covering representations, operations, Euler's formula, and de Moivre's theorem. Ideal for beginners and as a refresher for advanced learners.
Why Are There No 3 Dimensional "Complex Numbers"?
Explores the mathematical reasons behind the absence of 3D complex numbers, delving into algebra, quaternions, and the limitations of number systems beyond 2D complex planes.
Geometric Langlands over F_q
Explore strategies to deduce geometric Langlands conjecture for ℓ-adic sheaves, connecting F_q and complex number theories in advanced mathematics.
Complex Analysis - Roots of Unity and Rational Powers of Z
Explore complex logarithms and exponentials to compute fractional powers of complex numbers, including nth roots of unity and special cases like the square root of i.