Prove that:
(a) If f(z) and f(z) bar both are analytic in a domain, then it is a constant function
(b) If f(z) is analytic in a domain D and f'(z) = 0 in D. then it is a constant function.
(c) If f(z) is analytic in a domain D and ux+vy = 0 in D, then f(z) is a constant function
(d) Let f(z) = u+iv =Re^(i.theta) be an analytic function in a domain D. If either of the functions u, v, R, theta, is a constant function in D, then f is a constant function.
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