Question 1:

Use Cauchy's Integral Formula and/or Cauchy's formula for derivatives when y = y(0; 2) to evaluate: + 5 1 dz, (izz) (z -1) 3edz, (i) dz, (iz) 2 - 2 22 +z+1 Y 1 dz. (iv) 2 2 (z - 1) -3dz , (v) ( 8 + 1) 2 ( 2 2 + 9 )Locate and classify the singularities (non-isolated, removable, poles of order m or isolated essential) in C of the following functions: 1 1 23(22 + 1) (ii) ( 2 2 + 2 + 1 ) 5 (izi) 1 1 1 - ez (iv) (z + 7/2) (1 - cos z) 2