An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y), where $${\text{i}} = \sqrt { - 1} .$$   If u(x, y) = x² - y², then expression for v(x, y) in terms of x, y and a general constant c would be

A. xy + c

B. $$\frac{{{{\text{x}}^2} + {{\text{y}}^2}}}{2} + {\text{c}}$$

C. 2xy + c

D. $$\frac{{{{\left( {{\text{x}} - {\text{y}}} \right)}^2}}}{2} + {\text{c}}$$

Answer: Option C