CVR15

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Find the residues of f(z)\, at all its isolated singular points and at infinity (if infinity is not a limit point of singular points), where f(z)\, is given by \frac{\sin z}{z^2+4}\,

The poles are at z=\pm2i\,.

\lim_{z\to 2i} \frac{\sin z}{z+2i} = \frac{\sin 2i}{4i} = \frac{\sinh 2}{4}\,

\lim_{z\to -2i} \frac{\sin z}{z-2i} = \frac{\sin -2i}{-4i} = \frac{\sinh 2}{4}\,


Main Page : Complex Variables : Residues

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