The locus of points $z$ in the complex plane that satisfy $z \bar{z}+z+\bar{z}=3$ is
(A) a line
(B) a semicircle
(C) a circle
(D) an ellipse
5. (C).

The condition is $(z+1)(\bar{z}+1)=4$, which means $|z+1|=2$, this is a circle.