The complex variable boundary-element method is routinely used to determine the complex potential, θ = φ + ¡ψ , at any position, z = x + iy, internal to the flow domain. We reverse this mapping by exactly determining the complex position for specified complex potentials––in effect solving for z(θ) instead of θ(z). Direct calculation of the physical location, [x,y], of potential, [φ , ψ] , intersections greatly simplifies the determination of groundwater flownets and travel times. One problem arises when overlapping sheets in the complex potential domain form due to multiple capture zones, with dividing stream lines forming branch cuts. We avoid this problem by resolving individual capture zones, and then determining the flownet within each zone. Travel times are readily calculated using increments in potential along a streamline. Examples of flow under a dam, free surface delineation within a dam, regional flow, and dipole flow are used to demonstrate the method s utility. ®2003 Elsevier Science Ltd. All rights reserved.