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Unformatted text preview: 20052 122 (B) 2 2_ * 1. 2 33 i -1 213 . f ( z ) = a ln( x 2 - y 2 ) + i arctan y x (1 + 4iz 3 )dz 2.2 a = x >0z . 3. 2 f ' (1 - i ) f ( z) f ( z) = C 3 2 + 7 + 1 d -z 2 C : z* = 3 (_ ( z - 1) n =1 z n2 4. 1 Lau ren t n 1 n + z - 1) n n ( n = 0 [2 + ( -1) ] * _ 5. 2 f ( z) = e1- z ez -1 # . * ( _ 3 Re w > 0 f ( z ) = 1, arg f '(0) = * 6. ( _ P6 ! # 1. 2. 3._ 4 . _ w = f ( z) | z |< 2 2 ,2 f ( z) = . 83 16 _ * . Morera 2 . Cauchy 2 . sin 1 c z 4 dz 2 z -1 CX Xi 1 - 1 5 . 2 | z | =3 z13 dz ( z 2 + 5)3 ( z 4 + 1) 2 5 3 + 0 x sin 3x dx (x2 + a2 ) ( a > 0) z 5 f (z) = 1 z 2 - 3z + 2 z 1 i V z >2 8 z 2~ i V 0< z -2 <1 * i V z < 2,0 < arg z < 4 ( ) 8 * 12 . 8~ $ i V P * ` ( 1 ) L i ouv i l l e (2 ) Rouchez z 10 . 9 z + e- z = a, (a > 0) Re z > 0 ` * 10 . ...
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This note was uploaded on 05/12/2008 for the course IS 102 taught by Professor Mrkai during the Spring '08 term at Shanghai Jiao Tong University.

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