If a function $\displaystyle f(z) = u(x,y) + iv(x,y)$ is analytic in some domain in the complex plane.

How can we show that families of the level curves $\displaystyle u(x,y) = c_1$ and $\displaystyle v(x,y) = c_2$ are orthogonal.

Also, point z_0 of intersection of two curves $\displaystyle u(x,y) = c_1$ and $\displaystyle v(x,y) = c_2$ that the tangent lines are perpendicular if f'(z) is not 0.

For this do I just find u' and v' and then apply Cauchy - Riemann eqns??