Which of the following is/are) correct:

A. If U = x² - y² is real part of an analytic function f(z) then analytic function f(z) = z + c

B. Zeros of cosz is \(\pm(2 n-1) \frac{π}{2}\), where n = 1, 2, 3,

C. If f is entire and bounded for all values of z in the complex plane, then f(z) is constant throughout the plane.

D. \(\int_C \frac{2 z+1}{z(z+1)} d z\) = πi, where |z| = \(\frac{1}{2}\) 

Choose the correct answer from the options given below: