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As i am new user at MSE i directly posted question without giving my attempt and question was closed but i actualy solved half part but unable to prove another....kindly solve my problem...

Ias 2014 complex numbers

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I solved the derivation part but unable to prove that the Ux=Vy AT f(0)...kindly direct me how to solve it..... I got Ux=(X^4 +3X^2Y^2 + 2XY^3)/(X^2 + Y^2)^2

Uy= -Y^4 -2X^3Y -3X^2Y^2)/(X^2 +Y^2)^2

Vx= (X^4 - 2XY^3 + 3X^2Y^2)/(X^2+Y^2)^2


and there is real question how to prove Ux=Vy at (x,y)=(0,0)