Solution
= Solution
The rotation $\nabla v=(-u_y,u_x)$ from the <Cauchy-Riemann equations> is invertible. Hence
$$
\boxed{\nabla u=0\quad\Longleftrightarrow\quad\nabla v=0.}
$$
Thus their <stationary points> coincide, including degenerate ones.
= Solution
The rotation $\nabla v=(-u_y,u_x)$ from the <Cauchy-Riemann equations> is invertible. Hence
$$
\boxed{\nabla u=0\quad\Longleftrightarrow\quad\nabla v=0.}
$$
Thus their <stationary points> coincide, including degenerate ones.