# Why do level curves of a function and its harmonic conjugate intersect each other orthogonally?

So I've had this assignment in which I had to proof that two level curves of a function and one of its harmonic conjugates intersect each other orthogonally.

The proof itself wasn't that difficult, but I wondered: why does this happen?

What is the underlying cause for this phenomenon?

This is a consequence of the Cauchy-Riemann equations: $$u_x=v_y,\\u_y=-v_x,$$ which imply that $$\nabla u \,\perp\, \nabla v.$$