For an analytic function f(z) on domain D which of the following is(/ are) correct:
(A). if Real part of f(z) is constant then f(z) is constant function.
(B). If |f(z)| is a non zero constant in D, then f(z) is constant function in D.
(C). If f'(z) = 0 everywhere in D then f(z) is constant function in D
(D). if |f(z)| is a non zero constant in D, then f(z) is constant only some z in D.
Choose the correct answer from the options given below:
1
(A), (B) and (C) only.
2
(A), (C) and (D) only.
3
(A) and (D) only.
4
(D) only.