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Pure Mathematics

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

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.

Details
Parent Category: 4 Complex numbers
Category: 4.1 Complex numbers expressed in Cartesian form
Hits: 1124

Details
Parent Category: 4 Complex numbers
Category: 4.1 Complex numbers expressed in Cartesian form
Hits: 10777

From Coordinates to Polar Meaning: An AI Argand Observatory

Argand Modulus and Argument Observatory develops Representation of complex numbers in the Argand diagram, finding the modulus and argument of a complex number through six visual, misconception-first stages.

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.

Details
Parent Category: 4 Complex numbers
Category: 4.2 Complex numbers expressed in polar form
Hits: 1098

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Parent Category: Pure Mathematics
Category: 5 Calculus
Hits: 7568

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Parent Category: Pure Mathematics
Category: 5 Calculus
Hits: 9820

  1. Definite Integral JavaScript Simulation Applet HTML5
  2. Integral: Algorithms of Numerical Approximation JavaScript Simulation Applet HTML5
  3. Differential Quotient JavaScript Simulation Applet HTML5
  4. 📈Exploring Numerical Approximations to Ordinary Differential Equations with Slope Fields JavaScript Simulation Applet HTML5

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

5 Calculus Article Count:  14

5.5 Differential equations Article Count:  9