IB Maths AI HL Complex Numbers – HL Unit 2: Cartesian, polar and Euler forms, phasors, IB test

A complete, ready-to-teach unit of additional higher level content for IB DP Mathematics: Applications and Interpretation HL, Topic 1 (AHL 1.12, 1.13). Four animated lessons: the unit covers Cartesian form and complex roots of quadratics, the complex plane with modulus and argument, polar and exponential forms, and applications: rotations and adding sinusoids with phasors. An IB-style unit test then checks what students have learned.
Animated slides that teach step by step
Every question appears first. Each click fades in the next line of working or the next answer, so you can ask students to predict the next step before you reveal it. A PDF copy of each deck shows every answer: ideal for cover lessons, revision and absent students.
What’s included
• 4 lessons (52 slides): Complex Numbers in Cartesian Form; The Complex Plane, Modulus and Argument; Polar and Exponential Forms; Rotations and Adding Sinusoids
• Each lesson: starter, key ideas (formula booklet references), 4 worked examples with GDC steps, ‘your turn’ questions, an exam-style question with an IB-style markscheme, an exit ticket and a summary
• Speaker notes on every slide with a short script and all the answers
• 4 worksheets (Word + PDF): fluency, problem solving and exam-style questions, with full answers
• Unit test (60 minutes, 50 marks): Section A short response (Paper 1 style) and Section B extended response (Paper 2 style), GDC throughout, editable in Word
• Full markscheme in IB notation (M1, A1, R1, AG) with indicative grade boundaries
• Teacher guide: lesson plans with timings, syllabus map, subject knowledge, common misconceptions, support and stretch ideas, and the full AI HL course plan
Exam-ready
Questions are labelled Paper 1 style (short response) or Paper 2 style (extended response), with a GDC allowed throughout as in every AI exam. Argand diagrams accompany the key examples, and the AC-circuit questions show the AI-specific use of complex numbers. All questions are original and every answer has been checked.
Written to the current AI guide (first assessment 2021, final exams November 2028). This is HL Unit 2 of 11 HL units; the shared SL/HL core is in the AI SL Units 1–12.
Independent resource: not produced or endorsed by the International Baccalaureate Organization.