Math Problem Statement

Find where the Mobius transformation f(z)=1+z/1-z maps the unit circle , the real axis and the imaginary axis

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Analysis
Möbius Transformation
Geometric Mappings

Formulas

Möbius transformation: f(z) = (1 + z)/(1 - z)
Euler's formula: z = e^(iθ) for points on the unit circle
Trigonometric identities: e^(iθ) - e^(-iθ) = 2i*sin(θ) and e^(iθ) + e^(-iθ) = 2*cos(θ)

Theorems

Properties of Möbius transformations (angle-preserving, mapping of lines and circles)

Suitable Grade Level

Undergraduate Level - Complex Analysis