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  4. A.5 Complex Numbers, Induction, and Linear Systems
Topic 05Mathematics: Analysis and Approaches

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.

Practice questions
1

Complex numbers in Cartesian formHLSign up

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

35 min
2

Modulus–argument (polar) form and Euler formHLSign up

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

40 min
3

De Moivre's theorem and complex rootsHLSign up

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

40 min
4

Proof by induction, contradiction, and counterexampleHLSign up

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

50 min
5

Systems of linear equationsHLSign up

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

35 min

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A.4 Binomial Theorem and Counting

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B.1 Function Foundations