If(z) = u(x, y) + iv(x, y) is an analytic function or complex

If(z) = u(x, y) + iv(x, y) is an analytic function or complex variable z = x + iy where i = √-1 , u (x, y) = 2 xy, then v(x, y) may be expressed as

1. -x² + y² + constant
2. x² - y² + constant
3. x² + y² + constant
4. -(x² + y²) + constant

Given f(z) = u + iv is analytic and u = 2xy We know that if f(z) is analytic then CR equations will be satisfied.

i.e.	∂u	=	∂v
	∂x		∂y

and	∂u	= -	∂v
	∂y		∂x

Verify the options which satisfy the above C-R equations.
v = – x² + y² + constant, satisfies the C-R equation.