= Orthogonal level curves of harmonic conjugates
For a <holomorphic function> $f=u+iv$, the <Cauchy-Riemann equations> imply $\nabla u\cdot\nabla v=0$ and $|\nabla u|=|\nabla v|=|f'|$. At a point where $f'\ne0$, the two regular level curves therefore meet at right angles, since each tangent is perpendicular to its nonzero gradient. The noncritical condition is necessary: for $f(z)=z^2$, the zero level sets are the coordinate axes and the two diagonals, which meet at angles of $\pi/4$ at the critical point zero. Orthogonality at regular points is one geometric expression of conformality.
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