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(Solved): Problem 2. (i) Show That Cos(2) Tends To Too As [2] + Too Along A Straight Line Through ( With Non-z...


Problem 2. (i) Show that cos(2) tends to too as [2] + too along a straight line through ( with non-zero slope Hint: Write z =

Problem 2. (i) Show that cos(2) tends to too as [2] + too along a straight line through ( with non-zero slope Hint: Write z = reio with 0 + nn fixed and let r + (ii) Show that sin(z) is real if and only if either Im(z) = 0 or Re(2) = n(n+ (1/2)), n e Z. 03 Problem 3. Find a (piecewise) smooth parametrization of the fol- lowing contours: (i) The curve in the figure to the right (ii) The ellipse = 1 (where z = x + iy), running once from zi = a to itself with the positive orientation. CX2 21 = 2 R


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