"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert. "Face problems with a minimum of blind calculation, a maximum of seeing thought" – Hermann Minkowski

Video clips on geometric method for Möbius transformations

Geometric method for Möbius transformations: rules for calculation

Geometric method when pole is on the z-locus
Geometric method when z-locus is a line
What you must write to explain and justify the geometric method
Why the geometric method works: intersecting chords theorem
Why the geometric method works: intersecting secants theorem
Why the geometric method works: circle inversion theorem needed when z-locus is a line
When you want to find the locus of z given |z-a| = c|z-b|. Alternative methods. Circle of Apollonius.