Mechanical Engg. (GATE) 2009

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Multiple Choice

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv (x, y) where i = $\sqrt{-1}$
If u = xy, the expression for v should be

  1. $\frac{(x + y)^2}{2} + k$
  2. $\frac{x^2 - y^2}{2} + k$
  3. $\frac{y^2 - x^2}{2} + k$
  4. $\frac{(x - y)^2}{2} + k$
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