Hi All, I was reading through Kreyzeig's Advanced Engineering Mathematics and came across two theorems in Complex Analysis. Theorem 1: Let f(z) = u(x,y) + iv(x,y) be defined and continuous in some neighborhood of a point z = x+iy and differentiable at z itself. Then, at that point, the first-order partial derivatives of u and v exist and satisfy the Cauchy–Riemann equations. Theorem 2: If two real-valued continuous functions and of two real variables x and y have continuous first partial derivatives that satisfy the Cauchy–Riemann equations in some domain D. Then the complex function is analytic in D. It seems that the hypothesis of Theorem 1 is similar to the conclusion of Theorem 2. Can these two theorems be modified into one iff statement? Thanks.