Public learning track
Complex Polynomials and the Fundamental Theorem of Algebra
11th Grade · Math · Open Global Math
8 lessons
Goal
Apply the Fundamental Theorem of Algebra, factor polynomials completely over the complex numbers, and solve higher-degree equations.
Featured Diagrams
The Fundamental Theorem of Algebra and Quadratic Equations
8 lessons
0 of 8 done
- 1The Fundamental Theorem of Algebra and Quadratic EquationsUp nextStart
- 2The Conjugate Root Theorem for Polynomials with Real CoefficientsPremiumNot started yet
- 3Solving Polynomial Equations with Real and Complex RootsNot started yet
- 4Using Structure to Factor Higher-Degree PolynomialsNot started yet
- 5Complete Linear Factorization over the Complex FieldNot started yet
- 6Vieta's Formulas Relating Complex Roots and Polynomial CoefficientsNot started yet
- 7Constructing Polynomials from Specified Complex RootsNot started yet
- 8Solving Cyclotomic and Polynomial Systems in the Complex FieldNot 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.