  According to Bohr's principle of complementarity, a quanton can behave either
as a wave or a particle, depending on the choice of the experimental setup.
Some recent two-path interference experiments have devised methods where one
can have a quantum superposition of the two choices, thus indicating that a
quanton may be in a superposition of wave and particle nature. These
experiments have been of interest from the point of view of Wheeler's
delayed-choice experiment. However, it has also been claimed that this
experiment can violate complementarity. Here we theoretically analyze a
multipath interference experiment that has a which-path detector in a quantum
superposition of being present and absent. We show that a tight multipath
wave-particle duality relation is respected in all such situations, and
complementarity holds well. The apparent violation of complementarity may be
due to incorrect evaluation of path distinguishability in such scenarios.
