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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(4) Let ƒ₂ = 0ƒ/əz and ƒz = 0ƒ/əz. Recall f = u + iv, the notation f is used for the complex conjugate function u - - iv. (d) The Jacobian of f, viewed as a map U → R², is defined by Jf = det (Df). Show that Jf = |fz|² - |fz|². In particular, if ƒ € O(U), then Jƒ = |ƒ'|².
Transcribed Image Text:(4) Let ƒ₂ = 0ƒ/əz and ƒz = 0ƒ/əz. Recall f = u + iv, the notation f is used for the complex conjugate function u - - iv. (d) The Jacobian of f, viewed as a map U → R², is defined by Jf = det (Df). Show that Jf = |fz|² - |fz|². In particular, if ƒ € O(U), then Jƒ = |ƒ'|².
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