Argand Operations
Separate addition as translation from multiplication as rotation and dilation; use conjugation as reflection.
Edexcel IAL Further Mathematics
Complex
Motion
Keep one Argand language while arithmetic becomes motion, equations become regions, and the extended plane closes onto the Riemann sphere.
08 ready00 queued4-7 min each
Instrument catalogue
de Moivre Root Wheel
Generate all fifth roots from indexed arguments, close the regular polygon, and raise every root back to the target.
Roots Move in Pairs
See why real coefficients force conjugate roots and which real transformations preserve their symmetry.
Modulus and Argument Loci
Carry one open region through recentering, rotation, scaling, and reciprocal inversion.
Apollonius Loci
Move from the equal-distance bisector to a verified ratio circle and sparse combined conditions.
Generalised Circle Mappings
Compare affine, reciprocal and Möbius images while naming the pole explicitly.
Möbius Geometry Toolkit
Use exceptional points, conformality and pole geometry to classify line/circle images and construct image centres and diameters.
The Riemann Sphere
Match tangent-plane points to the sphere, close infinity at the north pole, and turn the general circle theorem into a rigid-rotation example.