  We present a novel complex number formulation along with tight convex
relaxations for the aircraft conflict resolution problem. Our approach combines
both speed and heading control and provides global optimality guarantees
despite non-convexities in the feasible region. As a side result, we present a
new characterization of the conflict separation condition in the form of
disjunctive linear constraints. Our formulation features one binary variable
per pair of aircraft, is free of trigonometric functions, and captures the
non-convexity in a set of quadratic concave constraints. Using our approach, we
are able to close a number of open instances and reduce computational time by
up to two orders of magnitude on standard instances.
