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.
Equality of complex numbers
What is groundbreaking here?
The activity turns equality from a procedural statement into a two-channel comparison: real parts must match and imaginary parts must match. Learners see exactly which component fails and receive targeted remediation instead of a generic incorrect message.
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
- Match componentsWhen does a + bi = c + di?
- Use conjugacyIf z = z*, what can you conclude?
- Recover coefficients1 + 2i is a root of 2z² + pz + q = 0, where p,q are real. Find p and q.
- Square rootsSolve z² = 3 + 4i.
- Cube rootsWhich set contains all roots of z³ = −8?
- Solve a systemSolve z + iw − 1 + i = 0 and 3z + 2w* − 4i = 0.
From a Word document to an expert learning experience
2. Add a learning-design prompt
Design a real-versus-imaginary component comparator. Require separate evidence for both components, visual alignment of equal parts, equations with unknowns, misconception-specific feedback, and a final generalisation that two complex numbers are equal exactly when both corresponding components are equal.
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
Have students cover one component at a time and explain why a match in only the real or only the imaginary part is insufficient.
- 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 GeneratedSLSEquality