Discussion
The bilinear transformation \( w = \dfrac{az + b}{cz + d} \) with \( ad - bc \neq 0 \) carries circles and lines to
Answer: B
A bilinear map is a composition of translations, scalings, rotations and the inversion \( z \mapsto 1/z \), and each of those carries the family of circles-and-lines to itself. Treating a line as a circle through the point at infinity makes the statement exact, and the condition \( ad - bc \neq 0 \) is what stops the map collapsing to a constant
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