hw1 - Note that in the second part a b c are complex not...

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Mathematics 185 – Intro to Complex Analysis Fall 2005 – M. Christ Problem Set 1 Problem sets will ordinarily be due each Tuesday. GSI Aubrey Clayton holds office hours on Mondays, for discussion of the problem set due the following day. Notation : x.y denotes exercise y of chapter x . Please read Chapters 0 and 1 of our text right away. We’ll begin Chapter 2 by Thursday September 1. Due Tuesday September 6: Problems 1.3, 1.4(i), 1.5, 1.7 (i,iii,vi,vii), 1.10, 1.12 (One way to do the first part is to use polar coordinates, de Moivre’s theorem, and the half-angle trig identites.
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Unformatted text preview: Note that in the second part, a, b, c are complex, not necessarily real.) 1.16 (You’re asked to show that for any circle C not containing-δ/γ , the image set φ ( C ) is equal to some circle.) • Also problems 2.2 (prove (i) only), 2.3 (i), 2.5 (Assume that the domain T of g is an open subset of C ; use Corollary 2.5 rather than the ε – δ definition of continuity.) • Read Chapter 2. Warning: Stewart and Tall sometimes write (a), (b), et cetera when they mean (i), (ii), et cetera....
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