Are we supposed to roll Complication on a failed Check? It doesn't state that under Check, but there's a reference to it on Resource Tracks (page 3).
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Right, so when a check results in a 1-4, there's a complication. There is also a complication when you refocus.
That being said, you don't need to roll for complication, necessarily. The complication rolling tables are suggestions. What's important is that you tick a resource track and that you explain in the fiction what was the cost of your action.
Hope that clears things up!