Prove the statement in Prob 27 for general k 1, 2, Use the Taylor series Data from Prob 27 Let f(z) be analytic at z 0 Suppose that f '(z 0 ) 0, , f (k 1) (z 0 ) 0 Then the mapping w f(z) magnifies angles with vertex at z 0 by a factor k Illustrate this with examples for k 2, 3, 4

Question: Prove the statement in Prob. 27 for general k = 1, 2, . Use the Taylor series. Data from Prob. 27 Let f(z)

Prove the statement in Prob. 27 for general k = 1, 2, · · ·. Use the Taylor series.

Data from Prob. 27

Let f(z) be analytic at z₀.Suppose that f'(z₀) = 0, · · ·, f^(k-1)(z₀) = 0. Then the mapping w = f(z) magnifies angles with vertex at z₀ by a factor k. Illustrate this with examples for k = 2, 3, 4.

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By the Taylor series since the first few derivatives vanish at z 0 fz fz 0 z z 0 k gz gz 0 0 ... View full answer

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