A.5 Complex Numbers, Induction, and Linear SystemsHL

Complex numbers in Cartesian formHLSign up

Complex numbers — z = a + bi · Arithmetic in Cartesian form

Modulus–argument (polar) form and Euler formHLSign up

Modulus and argument — the polar view · Multiplication, division, and powers in polar/Euler form

De Moivre's theorem and complex rootsHLSign up

De Moivre's theorem and integer powers · nth roots and conjugate-pair roots

Proof by induction, contradiction, and counterexampleHLSign up

Proof by mathematical induction · Proof by contradiction · Counterexamples to disprove universal statements

Systems of linear equationsHLSign up

Solving 3×3 linear systems by elimination · Classifying systems — unique, no, or infinitely many solutions