Unformatted text preview: ≤ y≤ π with no restriction on x . 4. Describe how to construct Riemann surfaces for the functions z( w ) given by the solu- tions of the following equations (a) w= z 4 (b) w = ( z- 1)5 / 2 5. Show that e z =e ¯ z. 6. Sketch the image under the map w = log z of each of the following figures (a) half disk | z | < 1, Re z > 0 , (b) vertical line y = e . 7. How would you make a branch cut to define a single-valued branch of the function log( z + i- 1). How about log( z- z )?...
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- Fall '07
- Unit Circle, Ring, Peter Koroteev