Analytic Functions practice

For $c_{1}, c_{2} \in \mathbb{C}$, the level curves $u = c_{1}$ and $v = c_{2}$ are orthogonal wherever they intersect.

$\nabla{}u \cdot \nabla{}v = 0$ at every point.

If f is an entire function, then $\nabla{}u \cdot \nabla{}v = 0$ at every point.

If $\nabla{}u \cdot \nabla{}v = 0$ at every point, then f is an entire function.