Let f: C → C be differentiable at zo. Considering f as a map R? → R², that f'(zo) = kR where k is a non-negative constant, and R is a 2 x 2 rotation matrix; that is, a matrix of the form prove cos(0) – sin() sin(0) cos(0) where 0 E (-n, 7]. If f = u + iv for functions u, v: R² → R, what are k and Rin terms of u and v?

Let f: C → C be differentiable at zo. Considering f as a map R? → R², that f'(zo) = kR where k is a non-negative constant, and R is a 2 x 2 rotation matrix; that is, a matrix of the form prove cos(0) – sin() sin(0) cos(0) where 0 E (-n, 7]. If f = u + iv for functions u, v: R² → R, what are k and Rin terms of u and v?

Name: Let f: C → C be differentiable at zo. Considering f as a map R? → R²,
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Description: Let f: C → C be differentiable at zo. Considering f as a map R? → R²,that f'(zo) = kR where k is a non-negative constant, and R is a 2 x 2 rotationmatrix; that is, a matrix of the formprovecos(0) – sin()sin(0) cos(0)where 0 E (-n, 7].If f = u + iv f

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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Question

Let f: C → C be differentiable at zo. Considering f as a map R? → R²,
that f'(zo) = kR where k is a non-negative constant, and R is a 2 x 2 rotation
matrix; that is, a matrix of the form
prove
cos(0) – sin()
sin(0) cos(0)
where 0 E (-n, 7].
If f = u + iv for functions u, v: R² → R, what are k and Rin terms of u and v?

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