1. Find the values of the integrals (i) S Re z dz (ii) Sa z2 dz...

 

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1. Find the values of the integrals (i) S Re z dz (ii) Sa z2 dz from the point z1 = 1 to the point z2 = i in the positive direction on the following curves C: (a) the boundary of the square: 0 <x < 1, 0 <y<1. Ans: (i) 1/2 +i (ii) = (b) the part of the circle: z = et, 0 <t < . Ans: (i) in/4 – 1/2 (ii) = -1-i 3 (c) the straight line segment z = (1 – t) + it 0 <t < 1. Ans: (i) = (ii) = -1+i 3 1. Find the values of the integrals (i) S Re z dz (ii) Sa z2 dz from the point z1 = 1 to the point z2 = i in the positive direction on the following curves C: (a) the boundary of the square: 0 <x < 1, 0 <y<1. Ans: (i) 1/2 +i (ii) = (b) the part of the circle: z = et, 0 <t < . Ans: (i) in/4 – 1/2 (ii) = -1-i 3 (c) the straight line segment z = (1 – t) + it 0 <t < 1. Ans: (i) = (ii) = -1+i 3