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If f(x, y) = (1+x+y)(1+x-y)+a(x^2-y^2)-1+2iy(1-x-ax) is a complex analytic function then find the value of a.

If f(x, y) = (1+x+y)(1+x-y)+a(x^2-y^2)-1+2iy(1-x-ax) is a complex analytic function then find the value of a.

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