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Let C represent the unit circle in the complex variable, z = x + iy. If f = cosh 3z, then ∮_C f(z) dz = ?

1. 0
2. 2πi
3. πi
4. 4πi

Correct answer: 0

Solution

The integral of a holomorphic function over a closed contour is zero if the function has no singularities inside the contour. Since cosh(3z) is an entire function (holomorphic everywhere), the integral over the unit circle is zero.

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