"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, the foremost mathematician of the 20th century, speaking as the Nazis neared power in his native Germany.

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.