Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Complex Analysis
Möbius Transformation
Conformal Mapping
Formulas
f(z) = (az + b) / (cz + d)
|z + 1| < 1
ad - bc ≠ 0
Theorems
Möbius Transformation Conditions
Geometric Properties of Möbius Transformations
Suitable Grade Level
University (Advanced Complex Analysis)