A.5 Complex Numbers, Induction, and Linear SystemsHL
(HL only) Complex numbers in Cartesian, polar, and Euler form; De Moivre and complex roots; proof by induction, contradiction, and counterexample; systems of linear equations.
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