If $u+\iota v$ is analytic function, then $dv$ is equal to:
My attempt: $dv=v_xdx+v_ydy$ and since $u+\iota v$ is analytics, C-R eqns are satisfies and we have $u_x=v_y$ and $u_y=-v_x$. So, $dv=-u_ydx+u_xdy$. But the solution key says the answer is:
$dv=-u_ydx-u_xdy$
What am I doing wrong here? Am I missing something important? Thanks for the help.