1).Problem. Calculate ln(2) and acos(2).

2. Problem . (a) Evaluate the integral: C dz f (z) , where f (z) = z and C is the closed path defined as the square with vertices (corners) at 1 i, 1 + i, 1 + i and 1 i. (b) Evaluate the integral of f (z) = z (the complex conjugate of z, also denoted as z in the textbook) along the same closed path.

3. Problem (30 points). Evaluate the integral: dx cos x/(x^4+ 1) using suitable contour integrations and the theorem of residues. Show clearly, step by step, how you must proceed.