CVXI7

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Evaluate \int_C \sin z dz, C\, starts at the origin, traverses the bottom half of a unit circle centered at z0 = 1 / 2 and then the line from z = 1 to z = iπ.

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 z dz\,

=-\cos z \Bigg|_0^{i \pi} = -\cos i\pi +1 = 1-\cosh \pi\,


Main Page : Complex Variables : Complex Integrals

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