A complication is a difficult circumstance or a confused condition, like the complication you cause when you invite a dozen strangers to Thanksgiving dinner.
Complications can range from the one your teacher faces when you lose your pet snake in the classroom to the complications that occur during surgery, making recovery more difficult. The plot of your favorite book probably involves several complications for the characters, events or situations that make the ending uncertain or create a dilemma. Complication comes from the Latin complicāre, "to fold together," which makes sense since something with many folds is more complicated than something that's flat.
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