Apply the theorem in Sec. 22 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 − ie−y cos x;
(d) f (z) = (z2 − 2)e−x e−iy.