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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

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 Correct Answer $$\frac{{{{\text{y}}^2} - {{\text{x}}^2}}}{2} + {\text{k}}$$

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