An analytic function of a complex variable z = x + iy is

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y)+ iv(x, y), where i = √-1. If u(x, y) = 2xy, then v(x, y) must be

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	and	∂u	= -	∂v
	∂x		∂y		∂y		∂x

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