Lesson Plan

• Describe rectangular and polar representations of a complex number and convert between them.
• Apply appropriate forms to perform addition, subtraction, multiplication, and division of complex numbers.
• Interpret geometric loci in the Argand plane using modulus‑argument equations.
• Use De Moivre’s theorem to compute powers and roots of complex numbers.
• Solve A‑Level style problems involving complex numbers and present solutions clearly.

• Projector or interactive whiteboard
• Prepared slide deck with Argand diagram visuals
• Worksheet containing conversion tables and practice problems
• Graph paper and coloured pens for sketching loci
• Scientific calculators (or app) for trigonometric calculations
• Exit‑ticket slips

Begin with a quick visual of an Argand diagram and ask students to identify the real and imaginary parts of a point. Recall that they already know rectangular form from previous work. State that by the end of the lesson they will be able to move fluently between forms, solve loci problems, and apply De Moivre’s theorem to powers and roots.

1. Do‑now (5'): Review of $z=a+bi$ and plotting points on the Argand diagram.
2. Mini‑lecture (10'): Converting rectangular ↔ polar forms; introduce $r$ and $\theta$ formulas.
3. Guided practice (10'): Students convert a set of numbers while teacher checks understanding.
4. Demonstration (10'): Multiplication and division in polar form using $r\operatorname{cis}\theta$.
5. Loci activity (10'): Small groups identify the geometric shape described by given modulus/argument equations and sketch them.
6. Worked example (10'): Solve $z^{3}=8i$ using De Moivre’s theorem, step‑by‑step.
7. Exit ticket (5'): Write one key conversion formula and one real‑world application of De Moivre’s theorem.

Summarise the main ideas: representation choices, when to use each form, and the power of De Moivre’s theorem for roots. Collect exit tickets to gauge mastery and assign homework: a worksheet with conversion, loci, and a De Moivre root problem.