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GATE2016-1-3

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$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as

  1. $-x^2 + y^2 + $ constant
  2. $x^2 – y^2 +$ constant
  3. $x^2 + y^2 +$ constant
  4. $-(x^2 + y^2) +$ constant
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