Question

2. Let C denote the circle \z - il = 3 and compute f(z)dz if (a) f(x) = 332 (b) f(z) = + C) f(z) = sin(22) (d) f(x) = 212 3.

2. Let C denote the circle \z - il = 3 and compute f(z)dz if (a) f(x) = 332 (b) f(z) = + C) f(z) = sin(22) (d) f(x) = 212 3.


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Answer #1

C: Iz-jl= 3 C1,0) (3,0) find 812)dza (0,-3)) (a) 8121= (2+3;)(Z-3i) 9+72 Z=-31¢ C os inside of C. Z= 3i EC oA intide of C. an= Ini x g(3.i) = anix (3i) 3i+3i 2ni x 3i x3 375 = 9(2) (b/ 8121= 1-7 where g(z)=-1 is anelytic in C. TEC Cinide of c) and By$(2/= ginlaz) is Qualsfic in C. * By Ganchys thearsem, 812) Sin(azldz = 0. et (d) 812= (Z-ija %3D9() (z-ij° where g(21= et is

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