Discussion
Under \( w = 1/z \), the image of the circle \( |z| = 2 \) is
Answer: D
Taking moduli, \( |w| = 1/|z| \), so
\[ |z| = 2 \quad \Longrightarrow \quad |w| \;=\; \tfrac{1}{2}. \]
The inversion turns the circle inside out about the unit circle, which is left fixed. A circle maps to a straight line only when it passes through the origin, where the map sends points to infinity
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