Let G be a domain and assume that f: G→ C is continuous. Deter- mine which of the following statements are true, and which ones are false. • If you think a statement is true, briefly explain your reasoning. • If you think a statement is false, you must prove it by providing a counterexample. Follow these directions carefully. (i) If f is holomorphic on G, then [ f(z) dz = 0 for any closed contour C lying in G. (ii) If f has an antiderivative on G, then [ƒ(z) dz = 0 for any closed contour in G. (iii) Suppose that f is holomorphic on G except for at a single point zo. Let CR be a positively oriented circle of radius R> 0 (small enough that the circle lies in D) centered at zo. Then Jc f(z) dz = lim limf(z) dz (iv) If f is holomorphic on G, then there exists a holomorphic function F: G → C such that F'(z) = f(z) for all z € G. (v) Let C be any circle with positive orientation and R the closed disk consisting of C and its interior. If f is entire and constant on C, then f is constant on R. (vi) If √f(z) dz = 0 for any closed contour C lying in G, then the real and imaginary parts of f satisfy the Cauchy- Riemann equations on G. (vii) If f is entire and n € Z>o, then there exists an entire function F such that F(") (z) = f(z) for all z € C (here F(") denotes the nth derivative of F).