Public learning track
Complex Numbers in Rectangular Form and the Argand Plane
11th Grade · Math · Open Global Math
8 lessons
Goal
Perform arithmetic on complex numbers in Cartesian form, compute modulus and conjugates, and graph loci in the Argand diagram.
Featured Diagrams
Defining the Imaginary Unit and the Complex Number System
8 lessons
0 of 8 done
- 1Defining the Imaginary Unit and the Complex Number SystemUp nextStart
- 2Powers of the Imaginary Unit and Cyclic PatternsPremiumNot started yet
- 3Algebraic Properties of Complex Number OperationsNot started yet
- 4Complex Conjugates and Properties of ConjugationNot started yet
- 5Dividing Complex Numbers Using ConjugatesNot started yet
- 6Modulus of Complex Numbers and the Triangle InequalityNot started yet
- 7Geometric Representation in the Argand DiagramNot started yet
- 8Loci and Regions in the Complex PlaneNot started yet
Curriculum Framework
11th Grade · Math · Open Global Math
1
7 lessons
Structure of Mathematical Proof: Direct Deduction and Exhaustion
Construct direct algebraic proofs, deductions from axioms, and proofs by exhaustion for finite cases and number-theoretic properties.
2
7 lessons
Proof by Contradiction, Contrapositive, and Disproof by Counterexample
Master indirect proof methods including contradiction, contraposition, and finding minimal counterexamples to refute conjectures.
3
6 lessons
Real Number Continuum: Density, Completeness, and Bounds
Analyze the topological structure of the real line, including Archimedean property, density of rationals, and the completeness axiom.
4
6 lessons
Advanced Surd Algebra, Rational Exponents, and Radical Conjugates
Manipulate complex surd expressions, apply index laws across all rational exponents, and rationalize multi-term radical denominators.
5
8 lessons
Complex Numbers in Rectangular Form and the Argand Plane
Perform arithmetic on complex numbers in Cartesian form, compute modulus and conjugates, and graph loci in the Argand diagram.
6
7 lessons
Polar and Exponential Forms of Complex Numbers
Convert between Cartesian, polar, and Euler's exponential forms, compute products and quotients, and evaluate powers via De Moivre's Theorem.
7
8 lessons
Complex Polynomials and the Fundamental Theorem of Algebra
Apply the Fundamental Theorem of Algebra, factor polynomials completely over the complex numbers, and solve higher-degree equations.