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Unformatted text preview: and are related by the equation = m + arg f ( m ) ( z ) . 3. Let C 1 and C 2 be two smooth arcs passing through the point z . Also let 1 and 2 be the image of C 1 and C 2 , respectively, under the transforma-tion w = f ( z ). In addition, let 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 1 and 2 as they pass through the point w = f ( z ) is equal to m . (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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- Fall '09