A.2 Logarithms, Complex Numbers, and MatricesHL
HL extensions of Number & Algebra. Laws of logarithms, simplification with rational exponents, the convergent infinite geometric series. Complex numbers in Cartesian, polar, and exponential forms with geometric meaning. Matrix operations, determinants, inverses for solving linear systems; eigenvalues and eigenvectors for diagonalization and Markov-chain analysis.
Logarithms and Rational ExponentsHLSign up
Laws of Logarithms · Rational Exponents
Infinite Convergent Geometric SeriesHLSign up
When Geometric Series Converge · Sum to Infinity Formula
Complex Numbers — Cartesian FormHLSign up
Real and Imaginary Parts, Cartesian Arithmetic · Argand Diagram and Complex Roots
Complex Numbers — Polar and Exponential FormHLSign up
Modulus, Argument, and Form Conversions · Geometric Multiplication
Matrices — Operations, Determinants, Inverses, Linear SystemsHLSign up
Matrix Operations · Determinant, Inverse, and Linear Systems
Eigenvalues, Eigenvectors, and DiagonalizationHLSign up
Eigenvalues from the Characteristic Equation · Eigenvectors and Diagonalization