Further Mathematics/Complex instrument 05

01/ 07

Ratio as a mapping

Turn a distance ratio into a modulus

A difficult locus becomes a centred circle in another plane.

Track the same point under w=(z+2)/(z-2).

Teacher layers PA and PB arms Source and image traces Corresponding points Region probes Pole and infinity guide

Teacher cue

Ask why lambda=1 is the exceptional case. Do not answer until the moving unit circle approaches w=1 and its preimage escapes.

Keyboard: arrows change step, space plays or pauses motion, R resets.