4. True or false. No proof is needed. 2 points each. (a) ( ) For f (z) = u(x, y) iv(x, y), if u, v have partial derivatives and satisfy Cauchy- Riemann equations at z0, then f is differentiable at z0. (b) ( ) If C is a smooth curve and f (z) : C R is a continuous real-valued function, then the integral R C f (z)dz is a real number. (c) ( ) For any z = x iy, sinh z = sinh x cos y i cosh x sin y. (d) ( ) For any non-zero z1, z2, Log(z1z2) = Log(z1)Log(z2). (e) ( ) The set {z = x iy C, |x| > 1} is a domain. F F T F F Page 5