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Pure Mathematics
Argand Transformation Workshop develops Geometrical effects of conjugation, negation, addition, subtraction, and multiplication by i through six visual, misconception-first stages.
Five algebraic operations become transformations learners can predict and test: reflection, half-turn, translation, vector difference and a 90-degree rotation. The final synthesis uses these ideas to reason about area without coordinates.
- Details
- Written by Loo Kang Wee
- Parent Category: 4 Complex numbers
- Category: 4.1 Complex numbers expressed in Cartesian form
- Hits: 1124
Read more: Complex Operations as Geometry: An AI Argand Transformation Workshop
Conjugate-Root Polynomial Detective develops Conjugate roots of a polynomial equation with real coefficients through six visual, misconception-first stages.
A theorem becomes a consistency-checking tool. Learners use a visible missing mirror root to reconstruct factors, infer coefficients and audit claims about real-coefficient polynomials.
- Details
- Written by Loo Kang Wee
- Parent Category: 4 Complex numbers
- Category: 4.1 Complex numbers expressed in Cartesian form
- Hits: 1127
Read more: The Missing Root Detective: AI and the Conjugate-Root Theorem
Complex Arithmetic Vector Lab develops Four operations of complex numbers through six visual, misconception-first stages.
Addition, subtraction, multiplication and division are coordinated across symbolic steps and the Argand plane. The visual model lets learners see when an operation is component-wise, when multiplication mixes components, and why division needs a conjugate.
- Details
- Written by Loo Kang Wee
- Parent Category: 4 Complex numbers
- Category: 4.1 Complex numbers expressed in Cartesian form
- Hits: 1153
Read more: Making Complex Arithmetic Visible: An AI-Built Vector Lab
Complex Equality Component Balance develops Equality of complex numbers through six visual, misconception-first stages.
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.
- Details
- Written by Loo Kang Wee
- Parent Category: 4 Complex numbers
- Category: 4.1 Complex numbers expressed in Cartesian form
- Hits: 1135
Read more: Equality as Evidence: An AI Component Comparator for Complex Numbers
Conjugate Mirror Studio develops Conjugate of a complex number through six visual, misconception-first stages.
Conjugation is experienced simultaneously as an algebraic sign change and a geometric reflection in the real axis. This dual representation makes identities such as zz* = |z|^2 meaningful rather than merely symbolic.
- Details
- Written by Loo Kang Wee
- Parent Category: 4 Complex numbers
- Category: 4.1 Complex numbers expressed in Cartesian form
- Hits: 1139
Read more: Conjugation You Can See: AI-Designed Reflection on the Argand Plane
Subcategories
1 Functions and graphs Article Count: 12
1.1 Functions Article Count: 6
1.3 Equations and inequalities Article Count: 1
2 Sequences and series Article Count: 11
2.1 Sequences and series Article Count: 5
3 Vectors Article Count: 5
3.3 Three-dimensional vector geometry Article Count: 1
4 Complex numbers Article Count: 11
4.1 Complex numbers expressed in Cartesian form Article Count: 7
4.2 Complex numbers expressed in polar form Article Count: 1
5 Calculus Article Count: 14
5.5 Differential equations Article Count: 9