1. Read for intent
The Word document supplied the syllabus objective, mathematical language and question evidence. Each item was analysed for the concept, representation and likely misconception it could reveal.
Representation of complex numbers in the Argand diagram, finding the modulus and argument of a complex number
What is groundbreaking here?
Modulus and argument are learned as measurable geometric quantities attached to a point, not as disconnected formulas. Dragging, radius and angle cues coordinate Cartesian and polar descriptions while preserving exact values.
The AI did not merely generate answers. It translated a static assessment document into an instrumented learning progression: learners predict, attempt, receive misconception-specific feedback, open a visual tutorial, retry, and leave semantic evidence that a teacher can inspect.
The six-stage learning journey
- PlotPlace z = 2 + 2i on the Argand plane.
- Find modulusFind |−3 − √3 i|.
- Find argumentFind the principal argument of 2 + 2i.
- Compare distancesWhich complex number is closest to the origin?
- Connect conjugacyFor nonzero z,w with principal arguments, |z|=|w| and arg z=−arg w. What follows?
- ReconstructA complex number has modulus 4 and principal argument 2π/3. Which Cartesian form is correct?
From a Word document to an expert learning experience
2. Add a learning-design prompt
Create an accessible Argand observatory with tap, drag and keyboard placement. Make modulus a radius, argument an oriented principal angle, require quadrant reasoning before inverse tangent, compare distances using squared moduli, and reconstruct exact Cartesian form from polar data.
3. Build for the SLS frame
The payload is self-contained and responsive, with touch targets, keyboard access, read-aloud support, closed overlays on launch and no dependency on a network library.
4. Preserve proven xAPI know-how
The supplied reference ZIP was treated as a contract. lib/xapiwrapper.min.js, lib/xAPI.js and the injected xAPI head block were copied byte-for-byte; only the learning payload was redesigned.
How a teacher can use it
Ask students to estimate radius and angle visually before calculating, then explain any difference between the estimate and exact value.
- Use stages 1–2 for diagnosis before formal teaching.
- Ask students to narrate what changes in the visual model before they calculate.
- Use the tutorial and retry trail as evidence of self-correction, not just the final score.
- Upload the accompanying ZIP directly as an SLS interactive resource when xAPI evidence is required.
Quality evidence
Every activity was checked at desktop, mobile and narrow-phone sizes; incorrect-feedback, visual-tutorial and correct-retry paths were exercised; and the package validator confirmed six stages, root-level ZIP entries, offline assets and byte-identical xAPI integration.
MathematicsComplex NumbersAI GeneratedSLSArgand Diagram