Prove the statement in Prob. 27 for general k = 1, 2, . Use the
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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 the full answer
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