Unformatted text preview: θ and φ are related by the equation φ = mθ + arg f ( m ) ( z ) . 3. Let C 1 and C 2 be two smooth arcs passing through the point z . Also let Γ 1 and Γ 2 be the image of C 1 and C 2 , respectively, under the transforma-tion w = f ( z ). In addition, let α be the angle between C 1 and C 2 as the pass through z . Show how the relation obtained in Problem 2 implies that the corresponding angle between the curves Γ 1 and Γ 2 as they pass through the point w = f ( z ) is equal to mα . (Note that the transforma-tion is conformal at z when m = 1 and that z is a critical point when m ≥ 2.)...
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This note was uploaded on 02/21/2012 for the course MATH 118 taught by Professor Forde during the Fall '09 term at University of Houston.
- Fall '09