Problem 1748 (difficulty: 3/10)

Show that the map \(\displaystyle 1/z\) preserves cross-ratio, i.e. \(\displaystyle (\tfrac1{z_1},\tfrac1{z_2},\tfrac1{z_3},\tfrac1{z_4})=(z_1,z_2,z_3,z_4)\). Find other maps with this property.

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