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2002 ¸ 12 Z 4 12 { 9

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2002 ¸   12  Z 4 12 { 9 

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1.

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() e”__ z ∈ D(0, 1) \ @/ #Œ f(z) = f(z) s,

() †<Êú f(z) \¦ "é¶&h\"f "4/åLú„>h %i`¦M: —¸ŽH>ú z´Ãºs s

 1lxue”`¦˜Ð#Œ.

2.

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2z(1 − z)2_ –Ð|½Ó/åLú\¦½¨ #Œ.

3.

&hìr°úכ Z

|z|=1

1

z2sin zdz `¦½¨ #Œ.

4.

&hìr°úכ Z

|z−1|=1

1

1 + z5dz `¦½¨ #Œ.

5.

&hìr°úכ Z

0

1

1 + x6dx `¦½¨ #Œ.

6.

&hìr°úכ Z

0

1

x2+ 3x + 2dx `¦½¨ #Œ.

7.

Z…ØÔ¾ºsº hBn : n = 1, 2, . . . i HÄ»> _”`¦˜Ð#Œ.

8.

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4

Ÿ

¤™è†<Êú_ âĺ\¦q“§ #Œ [O"î #Œ.

9.

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10.

%ò%i {z : −π

4 < arg z <3

4π} \¦\P2; éߖ0A"é¶óøÍܼ–Ð ˜Ð?/H 1pxyŒ•©œ φ îrX< φ(eπi/4) = 0 s

“¦ φ0(eπi/4) > 0 “ כ `¦¹1Ô.

11.

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1 + αz2 õ

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Ÿ

¤™è¨î€ 0A\ Õª9.

12.

ìøÍ¨î€ Hu0A\"f &ñ_)a6£§†<Êú w =

Z z 0

√ 1 1 − ζ√

1 + ζ dζ, z ∈ Hu _

 ©œ`¦½¨ “¦, „éߖ 1pxyŒ•©œe”`¦˜Ð#Œ. s †<Êú_ %i†<Êú z = sin w `¦˜Ð#Œ.

13.

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1

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