From Example Problems
Jump to: navigation, search

Evaluate \int _{C}\sin zdz,C\, starts at the origin, traverses the bottom half of a unit circle centered at z_{0}=1/2 and then the line from z=1 to z=i\pi .

The sine function is entire so the integral between two points is path independent, so the integral can be written more simply as

\int _{0}^{{i\pi }}\sin zdz\,

=-\cos z{\Bigg |}_{0}^{{i\pi }}=-\cos i\pi +1=1-\cosh \pi \,

Main Page : Complex Variables : Complex Integrals