1. A multi-needle sewing machine, comprising: a plurality of needle bars to each bottom end of which a needle can be attached; a needle bar case in which the plurality of needle bars are disposed in a line and that supports the plurality of the needle bars movably in an up-and-down direction; a needle bar case moving device that, by moving the needle bar case, moves one of the plurality of the needle bars to an image capture position, the image capture position being a position that is located directly above a needle drop position that is a sewing position; and an image capture device that is provided in a position that is lined up with the plurality of the needle bars in the needle bar case, that is positioned in the image capture position by the needle bar case moving device's moving of the needle bar case, and that captures an image.