MATH 300 Midterm: MATH 300 2015 Winter Test 2
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Be sure this exam has 9 pages including the cover. Note the number of marks for each question. Check your answer very carefully. (work will be considered for this problem). (3 points) (a) Find all roots to the equation (z + 1)10 = z10. (3 points) (b) Then the residue of f at z = i, denoted as res(f ; i) is (b) (3 points) (c) Find a branch of log(z2 + iz 3) such that it is analytic at z = i, and nd its derivative at z = i. Compute r z i z3+4z2 dz where is the circle |z| = 10 traversed once counterclockwise. (3 points) (e) 2 dz for the principal branch of z. 2 along the line segment going from to i. 7 z (2 cos z 2+z2)2 dz where is the circle |z| = 1. You must write clearly your arguments and justify. (4 points) (a)
