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. -x² + y² + constant B. x² - y² + constant C. x² + y² + constant D. -(x² + y²) + constant

A. 1 + 6i B. 9 - 8i C. 9 + 8i D. 17 + 6i

A. $$2\sqrt 2 + 2{\text{i}}$$ B. $$\frac{{ - 1}}{2} + \frac{{{\text{i}}{{\sqrt 3 }^2}}}{2}$$ C. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{2}$$ D. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{8}$$

A. 2πnj B. 0 C. $$\frac{{\pi {\text{j}}}}{{2\pi }}$$ D. 2πn