An analytic function f(z) of complex variable z = x + iy may be written as f(z) = u(x, y) + iv(x, y). Then, u(x, y) and v(x, y) must satisfy,

A. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{x}}}}$$

B. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{x}}}}$$

C. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{x}}}}$$

D. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{x}}}}$$

Answer: Option C