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Course: MATH MATH 552, Spring 2001
School: USC
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Word Count: 170

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Analysis Spring Complex 2001 Homework I Due Friday April 13 1. Conway, Chapter 1, section 3, problem 3. 2. The equation az + b + c = 0 can have solution set consisting of a single point, or a z line in the complex plane. (a) Find necessary and sufficient conditions on the complex constants a, b, and c so that the solution set is a line. (b) Find the solution in the case it is a single point. 3. The next two...

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Analysis Spring Complex 2001 Homework I Due Friday April 13 1. Conway, Chapter 1, section 3, problem 3. 2. The equation az + b + c = 0 can have solution set consisting of a single point, or a z line in the complex plane. (a) Find necessary and sufficient conditions on the complex constants a, b, and c so that the solution set is a line. (b) Find the solution in the case it is a single point. 3. The next two questions pertain to the correspondence between the extended complex plane and the unit sphere in R3 given in Chapter section 1, 6. (a) Find the mapping of the sphere to itself induced by the following two mappings 1 of the (extended) complex plane to itself: inversion, in which z z for z = 0, 1 0 and 0 ; and inversion in the unit circle, where z z for z = 0, with 0 and 0 . (b) Show that non-zero complex numbers z and z correspond to diametrically opposed points on the sphere if and only if z z = -1. 4. Conway, chapter 3, section 1, problem 7. 5. Conway, chapter 3, section 2, problem 9. 6. Conway, chapter 3, section 2, problem 14.
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