Determine which of the following functions is entire (analytic on the whole complex plane). Prove your...

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Determine which of the following functions is entire (analytic on the whole complex plane). Prove your answer. Carefully state each theorem you are using. a) f(z) = x² + y² + i(2xy). b) f(x) = e(ª−y) sin(x + y) — ie(x−y) cos(x + y). Determine which of the following functions is entire (analytic on the whole complex plane). Prove your answer. Carefully state each theorem you are using. a) f(z) = x² + y² + i(2xy). b) f(x) = e(ª−y) sin(x + y) — ie(x−y) cos(x + y).

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