Math Problem Statement

Find the bilinear transformation which maps the points z = −i, 1, i onto w = −1, 0, 1 respectively.

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Analysis
Bilinear Transformations
Möbius Transformations

Formulas

w = (az + b) / (cz + d)
w = (z - 1) / (1 - z)

Theorems

Bilinear (Möbius) Transformation Theorem

Suitable Grade Level

Undergraduate Level (Complex Analysis)