Apply the given theorem to verify that each of these functions is entire:
(a) f (z) = 3x + y + i (3y - x)
(b) f (z) = sin x cosh y + i cos x sinh y
(c) f (z) = e-y sin x - i e-y cos x
(d) f (z) = (z2 - 2) e-x e-iy.
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Entire Functions are investigated. The solution is detailed and well presented.