These tiny “pests” — really harmless, nonbiting flies, but “pests” because they have no shame whatsoever in invading human bathrooms — seek water and dampness in drains, sewers, bathrooms, kitchens, and other human places. They can be annoying en masse — but I think they’re gorgeous singly and up close! Its wings are iridescent, look!
The long, many-segmented antennae are unique to this family of flies, and is where the suborder gets its name: Nematocera, long-horned flies. They are variously known as filter flies, sewer gnats, or sink flies. Because of their unique “furry” appearance, they are also known as moth midges or moth flies. There are 2,600 species described worldwide, with 112 in North America.
Adults and larvae both feed on bacteria, and are extremely difficult to kill. They are hard to drown and not affected by contact with most cleaning liquids such as bleach or even by boiling water. Eggs are resistant to heat and can withstand being dried out for a time. Ridding a drain of flies requires keeping the area clean for at least three weeks.
This is almost certainly Clogmia albipunctata, because of the white spots visible along the wing margin, but it might be a closely related species. Alas, further identification would involve dissection.