Discussion
Match the map with what it does to the unit circle. 1. \( w = z + 1 \) 2. \( w = 2z \) 3. \( w = 1/z \) P. Doubles its radius Q. Shifts its centre R. Leaves it fixed as a set
Answer: B
A translation moves the centre without changing the radius. A real scaling multiplies the radius. Inversion sends \( |z| = 1 \) to \( |w| = 1 \), so the unit circle is carried onto itself, though each point moves to its own conjugate reflection round it
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