 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2010/5/ii/a/solution

F (z) = z sin z + cos z

, since differentiation cancels the sine terms and leaves

F^{'} (z) = z cos z

. The curve runs from

- i

i

. Both terms of

F

are even, so

F (i) = F (- i)

\int_{γ} z cos z d z = 0.

 New to topics? Read the docs here!