1. The problem statement, all variables and given/known data Find the contour integral of Log(z). The contour is defined as: x^2 + 4y^2 = 4, x>= 0, y>=0 2. Relevant equations 3. The attempt at a solution parametrize the contour as z(t) = 2cos(t) + isin(t) 0 <= t <= pi/2 The contour integral = ∫Log(z(t))z'(t)dt I am having trouble finding Log(z(t)). Log(z(t)) = ln|z(t)| + iArg(z(t)) Would ln|z(t)| = ln|sqrt(1 + 3cos(t)^2)| and Arg(z(t)) = t?