Math Problem Statement
Find the bilinear transformation which maps 1,i,-1 to i,0,-i by using cross ratio
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Complex Analysis
Bilinear (Möbius) Transformation
Cross Ratio
Conformal Mapping
Formulas
Cross-ratio formula: (z1 - z3)(z2 - z4) / (z1 - z4)(z2 - z3)
Bilinear transformation: w = (az + b) / (cz + d)
Theorems
Bilinear transformations preserve cross ratios
Cross ratio theorem
Suitable Grade Level
Undergraduate (Mathematics or Engineering)
Related Recommendation
Solving Bilinear Transformation Problem: Mapping Points z = 1, i, -1 to w = 1, 0, -1
Mapping Points -1, 0, 1 Using Schwarz-Christoffel Formula
Understanding Bilinear Transformations with Fixed Points
Finding Fixed Points of Bilinear Map w = (2iz - 6) / (z - 3)
Complex Numbers: Polar and Rectangular Forms of z_1z_2/z_3 and Related Expressions