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PART D. COMPLEX ANALYSIS CHAPTER 12 Complex Numbers and Functions. \ Conformal Mapping Major Changes . The old chapter on conformal mapping has been absorbed into Chap. 12, beginning with a general introduction to conformality in Sec. 12.5, continuing with the conformal mapping of the elementary complex functions in Secs, 12.6-12.8 and concluding with a special section on linear fractional transformations (Sec. 12.9). This- gives a better understanding of those functions because we now discuss their geometric properties (their mapping properties) simultaneously with their analytic formulas, as we do it all the time in calculus. SECTION 12.1. Complex Numbers. Complex Plane, page 652 Purpose. To discuss the algebraic operations for complex numbers and the representa- tion of complex numbers as points in the plane. Main Content, Important Concepts Complex number, real part, imaginary part, imaginary unit The four algebraic operations in complex Complex plane, real axis, imaginary axis Complex conjugates Two Suggestions on Content 1. Of course, at the expense of a small conceptual concession, one can also start im- mediately from (4), (5), z=xt+b, P= -] and go on from there. 2. If students have some knowledge of complex numbers, the practical division rule (7) and perhaps (8) and (9) may be the only items to be recalled in this section. (But I personally would do ten minutes more in any case.) SOLUTIONS TO PROBLEM SET 12.1, page 656 2. iz = -2 + 4i,-1-โ14,24 53 4, -96 + 2807 6. -7 โ 264 8 -O.1 + 1.3% 10. (7 โ 241/625, (7 + 241/625 12. 29/25 i 14. 4x3y โ dxy3, 4x2y? 16. (x? โ y?WO? + y?) 173 docsity.com 
