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 = xy, the expression for v should be

A. $$\frac{{{{\left( {{\text{x}} + {\text{y}}} \right)}^2}}}{2} + {\text{k}}$$

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

C. $$\frac{{{{\text{y}}^2} - {{\text{x}}^2}}}{2} + {\text{k}}$$

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

Answer: Option C