Unformatted text preview: Find the principal value of h e 2 (-1-√ 3 i ) i 3 πi  Q4(a). State the Cauchy integral formula.  Q4(b). Show that if C is the boundary of the triangle with vertices at the point 0 , 3 i , and-4 oriented in the counterclockwise direction, the  | Z C ( e z-¯ z ; dz |≤ 60 Q4(c). Evaluate Z 1+ i ( x-y + 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 .  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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This note was uploaded on 05/14/2010 for the course MATHEMATIC mathe taught by Professor Xyz during the Spring '10 term at Birla Institute of Technology & Science.
- Spring '10