Final answer:
Georges Bizet's last complete composition was the opera Carmen, which premiered in 1875. It became one of the most celebrated operas after a mix of initial receptions and is notable for its engaging melodies and drama.
Step-by-step explanation:
The last complete composition of Georges Bizet was Carmen, which is an opera in four acts. It is one of the most frequently performed and popular operas in the classical canon. Carmen was first performed at the Opéra-Comique in Paris on March 3, 1875, and despite its initially mixed reviews, it has since become acclaimed for its melodies and dramatic narrative.
Bizet died unexpectedly after the 33rd performance of Carmen, at the young age of 36. The other options given in the question, such as The Pearl Fishers, are earlier works of Bizet, whereas The Barber of Seville is by Gioachino Rossini, and Swan Lake is a ballet composed by Pyotr Ilyich Tchaikovsky.