Dragonflies are four-winged insects that have the ability to control aerodynamic performance by modulating the phase lag (phi) between forewings and hindwings. We film the wing motion of a tethered dragonfly and compute the aerodynamic force and power as a function of the phase. We find that the out-of-phase motion as seen in steady hovering uses nearly minimal power to generate the required force to balance the weight, and the in-phase motion seen in takeoffs provides an additional force to accelerate. We explain the main hydrodynamic interaction that causes this phase dependence.