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hw3_3 - f z = | z | 2 is differentiable only at z = 0...

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Complex Variables Assignment 3.3 Spring 2011 Due September 19 Exercise 1. Let log w denote the branch of the logarithm with arg w (0 , 2 π ] and let w 1 / 2 = e 1 2 log w . Where is ( z 2 + 4) 2 continuous? What about ( z 2 - 1) 1 / 2 ? Exercise 2. Show that
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Unformatted text preview: f ( z ) = | z | 2 is differentiable only at z = 0. [ Suggestion: For z 6 = 0, use the fact that g ( z ) = z is differentiable but that h ( z ) = z is not .] Exercise 3. 1.5.7...
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