Complex Quadratic Root Explorer develops Complex roots of quadratic equations through six visual, misconception-first stages.
The discriminant, exact algebra and Argand locations are linked in one progression. Non-real roots become interpretable points with symmetry and magnitude, so the quadratic formula is not an isolated manipulation.
Learning objective: Complex roots of quadratic equations
Resource type: Accessible HTML5 mathematics interactive, teaching guide and SLS xAPI package
Launch interactive Teaching guide Download SLS xAPI ZIP
Why this representation matters
The discriminant, exact algebra and Argand locations are linked in one progression. Non-real roots become interpretable points with symmetry and magnitude, so the quadratic formula is not an isolated manipulation.
Six-stage learning journey
- Pure imaginary roots: Solve z² + 3 = 0.
- Quadratic formula: Solve z² − z + 1 = 0.
- Complex coefficient: Solve z² + iz − 7 = 0.
- Leading i coefficient: Solve iz² + 3z − 2i = 0.
- Square a complex number: The number z satisfies z² = 3 − 4i. Find both values.
- Reverse engineer: Which quadratic has roots 2+3i and 2−3i?
The AI learning-design prompt
Build from negative discriminants to exact complex roots and then plot the pair. Preserve plus-minus structure, show i squared reasoning, handle complex coefficients carefully, include reverse engineering from roots to a quadratic, and diagnose missing i, denominator and sign errors.
The AI read Liang Soon's Word document for mathematical intent, identified likely misconceptions, and converted a static question set into a sequence in which learners inspect, attempt, receive visual feedback, open a tutorial and retry.
How a teacher can use it
Pause after the discriminant is found and ask learners to sketch where the two roots should lie before completing the exact calculation.
- Use the first two stages as a diagnostic before formal instruction.
- Ask students to describe the visual change before writing the symbolic step.
- Use the misconception and retry trail as evidence of self-correction.
- Upload the accompanying ZIP to SLS when scored xAPI evidence is required.
What the xAPI package contributes
The supplied xAPI wrapper, integration script and launch contract were preserved. The redesigned mathematics experience is the payload; the proven wrapper connects it to SLS launch, scoring and semantic learning evidence.
Keywords: Mathematics, Complex Numbers, AI Generated, SLS, Quadratic Equations