Unformatted text preview: D = { z :  z  < 1 , Im z > } onto the unit disc U (i.e., a biholomorphic map D â†’ U ). 6. Let P ( z ) = z n + a 1 z n1 + Â·Â·Â· + a n be a polynomial and 0 < Î¸ < Ï€/ (2 n ). Show that e P ( z ) â†’ âˆž , as z â†’ âˆž ,  arg z  < Î¸, and e P ( z ) â†’ , as z â†’ âˆž ,  arg zÏ€/n  < Î¸. 7. Prove that if Q is any polynomial, then  Q ( z )1 z  â‰¥ 1 for some z with  z  = 1....
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 Spring '09
 Math, Complex number, Holomorphic function, Meromorphic function, Prof. Lempert

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