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Consider the mapzrarrz2nbspas a map from c to ca nbspwhat

M415 Problem Set 6

Consider the map(z)→(z^2) as a map from C to C.
1. (a) What is the image of a horizontal line? Sketch your answers.
2. (b) What is the image of a vertical line? Sketch your answers.
3. (c) When does the image of a horizontal line degenerate? When does the image of a vertical line degenerate?
4. (d) You should have found conic sections for your answers to parts (a) and (b). Find the foci of these conic sections.

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