What is the term for the discoloration of the body after death?

The term for the discoloration of the body after death is indeed referred to as lividity. This phenomenon occurs due to the pooling of blood in the lower parts of the body as the heart stops pumping blood after death. Gravity causes the blood to settle in the areas that are closest to the ground, resulting in a purplish discoloration of the skin. This change can provide valuable information during a forensic investigation, such as the positioning of the body at the time of death and the time elapsed since death.

Other terms listed in the options refer to different post-mortem changes. Exsanguination describes the loss of blood, typically due to hemorrhage, and does not relate directly to discoloration. Rigor mortis refers to the stiffening of muscles after death, caused by chemical changes in the muscle fibers. Algor mortis is the process by which the body loses heat following death, contributing to the determination of time of death but not to discoloration.