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

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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