Maths AI-HL 1.13.3 Exponential form of complex numbers

Exponential form of complex numbers – Maths IB AI – HL

🔍 Overview

This visually engaging Maths PowerPoint lesson introduces students to Euler’s exponential form of complex numbers, showing how to express any complex number z = a + bi  as z = r e^(iθ). The presentation walks learners through the conceptual link between Cartesian, polar, and exponential forms of complex numbers, making abstract algebraic ideas clear and accessible.

📘 What’s Inside

• Step-by-step explanation of how to convert between a + bi and re^(iθ)

• Clear visual breakdown of modulus r = ∣z∣ and argument θ = Arg(z)

• Worked examples with full calculator guidance (GDC steps included)

• Notes on principal arguments and radians mode setup

• Reverse conversion practice: from exponential to Cartesian form

• Printable summary for quick student reference

🎯 Learning Outcomes

By the end of the lesson, students will be able to:

• Understand and apply Euler’s formula e^(iθ) = cos⁡θ + i sin⁡θ

• Represent complex numbers in exponential form

• Move fluently between Cartesian, polar, and Euler representations

• Use their GDC effectively to compute modulus and argument

👩‍🏫 Why Teachers Love It

Designed for IB Applications & Interpretation HL, this resource saves teachers hours of preparation. Each slide includes clear explanations, diagrams, and calculator walkthroughs — ideal for classroom projection or self-study revision. Perfectly aligned with the IB Mathematics syllabus (Topic 1.13

Content:

• PowerPoint presentation
• Worksheet
• Answers sheet

File size:

• PPTX (523 KB)
• PDF (226 KB)
• PDF (210 KB)

Number of slides:

16 slides

Preview: