<Cauchy's integral theorem> states that a <holomorphic function> on a simply connected open region has zero <contour integral> around every closed piecewise smooth <contour> in that region. More generally the same holds for a <contour> homologous to zero in its domain of <holomorphy>. Having no singularity on the curve alone is insufficient: $1/z$ has a nonzero <contour integral> around the unit circle.

Solution

Past exam of the short options paper of the physics Prelims of the University of Oxford / 2019 / S1 / 3 / a / Solution

 Solution (source code)