Unformatted text preview: Find the principal value of h e 2 (1√ 3 i ) i 3 πi [2] Q4(a). State the Cauchy integral formula. [2] Q4(b). Show that if C is the boundary of the triangle with vertices at the point 0 , 3 i , and4 oriented in the counterclockwise direction, the [3]  Z C ( e z¯ z ; dz ≤ 60 Q4(c). Evaluate Z 1+ i ( xy + ix 2 ) dz ; along the real axis from z = 0 to z = 1 and along the parallel to imaginary axis from z = 1 to z = 1 + i . [4] Q5. Use residues to evaluate the integrals ( i ) Z C tan z dz, where C is the positively oriented circle  z  = 2. ( ii ) Z ∞ x sin2 xdx x 2 + 3 ( iii ) Z 2 π dθ 1 + a sin θ (1 < a < 1) [4+5+5]...
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 Spring '10
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 Math, Linear Algebra, Vector Space, Complex number, space V. Let

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