Math Problem Statement
Hello. Mobius transformation can map circles into lines. Let's start with equation of a circle in complex place |z-c|=r, where r is real and constant, c is complex and constant, z is complex variable. If we denote 1/z=u we can write |1-cu|=r*|u|. How can this be an equation of a line in complex plane?
Solution
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Math Problem Analysis
Mathematical Concepts
Complex Analysis
Möbius Transformations
Inversion
Geometry of Circles
Formulas
|z - c| = r
|1 - cu| = r |u|
u = 1/z
Theorems
Möbius Transformation
Inversion Mapping
Suitable Grade Level
Advanced Undergraduate or Graduate
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