Interactive Complex Numbers

This collection contains eight staged instruments for parts of complex-number geometry that benefit from motion. Each scene separates the construction from its conclusion: trace the transformation first, then return to the algebra.

Open the Complex Numbers instruments →

Included instruments

1. Argand Operations — distinguish translation from rotation and dilation, then interpret conjugation as reflection.
2. de Moivre Root Wheel — solve a fifth-root equation, power one root in five steps, and reveal the symmetry of all five roots.
3. Roots Move in Pairs — connect real coefficients with conjugate symmetry through geometric operations on the Argand plane.
4. Modulus and Argument Loci — watch recentering, rotation, scaling, and reciprocal substitution transform a boundary and its region.
5. Apollonius Loci — develop equal-distance and fixed-ratio loci before combining strict geometric conditions.
6. Generalised Circle Mappings — compare affine, reciprocal, and Möbius images while tracking exceptional points.
7. Möbius Geometry Toolkit — use conformality and pole geometry to classify line and circle images and construct centres and diameters.
8. The Riemann Sphere — connect stereographic projection, infinity, generalised circles, and the spherical interpretation of Möbius maps.

The instruments are designed for teacher-led classroom use. Their diagrams stay sparse by default, while optional layers expose auxiliary constructions when a full proof is needed. All mathematical rendering assets are stored locally with the site.