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Question

Complex integration - Cauchy's integral
1. Compute the integral (50%)
sin 72 + cos 722
Je (22 - 1) (2 - 1)
.dz
where the C is the circle: z - i = 3
Hint: check that
(23-1)(2-1)
22- 1
2. Compute the following integrals (apply Cauchy's integral theorem whenever applicable)
(50%)
(a) f cos zdz
(b) fc sec zdz
(c) Pc 72_72+12
(d) f Edz
where C is the unit circle |z| = 1

This is a... View the full answer

2
&quot; P( 2 ) 2
Sin 1 72 + Cus * 2 2
(22-1 ) (2-1 ).
: fez, has a simple poll of.
Z = b, I E C : 12- ;1 - 3
Res ( P( 2) , 2 2 42 ) 5
Sin A + Cos A
2 - 212 .
- 1/2
Rus ( f(2) , 2 21 ) =
srina +...

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