4) Let ƒz = dƒ/əz and ƒz = 0ƒ/əz. Recall ƒ = u + iv, the notation f is used for the complex conjugate function u – iv. (d) The Jacobian of ƒ, viewed as a map U → R², is defined by Jƒ = det(Dƒ). Show that Jƒ = |f₂|² − |fz|². In particular, if ƒ ≤ O(U), then Jƒ = |ƒ'|².
4) Let ƒz = dƒ/əz and ƒz = 0ƒ/əz. Recall ƒ = u + iv, the notation f is used for the complex conjugate function u – iv. (d) The Jacobian of ƒ, viewed as a map U → R², is defined by Jƒ = det(Dƒ). Show that Jƒ = |f₂|² − |fz|². In particular, if ƒ ≤ O(U), then Jƒ = |ƒ'|².
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
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