4.1 Complex numbers expressed in Cartesian form

Making Complex Arithmetic Visible: An AI-Built Vector Lab

Expired

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.

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Category: 4.1 Complex numbers expressed in Cartesian form
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Equality as Evidence: An AI Component Comparator for Complex Numbers

Expired

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.

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Category: 4.1 Complex numbers expressed in Cartesian form
Hits: 4139

Conjugation You Can See: AI-Designed Reflection on the Argand Plane

Expired

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.

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Category: 4.1 Complex numbers expressed in Cartesian form
Hits: 4096

When Quadratics Leave the Real Line: An AI Complex-Root Explorer

Expired

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.

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Category: 4.1 Complex numbers expressed in Cartesian form
Hits: 3781

The Missing Root Detective: AI and the Conjugate-Root Theorem

Expired

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.

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Category: 4.1 Complex numbers expressed in Cartesian form
Hits: 3688

  1. Complex Operations as Geometry: An AI Argand Transformation Workshop
  2. 🔢Complex Number Graphical Calculator JavaScript Simulation Applet HTML5

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