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Which one of the following functions is analytic over the entire complex plane?

1. ln(z)
2. e^(1/z)
3. 1/(1-z)
4. cos(z)

Correct answer: cos(z)

Solution

The function cos(z) is entire, meaning it is analytic everywhere in the complex plane, as it can be expressed as a power series that converges for all z. In contrast, the other options have singularities or branch cuts that restrict their analyticity.

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