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Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is

1. cosh x exp(−iy)
2. cosh z exp z
3. cosh z cos y
4. cosh z

Correct answer: cosh z

Solution

The function f(z) is determined to be cosh z because it is analytic and its real part matches the expression for cosh x cos y, while the imaginary part being zero for y = 0 indicates that the function does not have any imaginary component at that line, consistent with the properties of the hyperbolic cosine function.

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