Final answer:
The period of time when syphilis symptoms improve or disappear completely is known as latent syphilis, which can last for months to many years.
Step-by-step explanation:
The period of time when symptoms improve or disappear completely, and may last for months to many years, is called Latent syphilis.
After the secondary stage of syphilis, the disease can enter a latent phase where there are no symptoms, but the bacteria are still present in the body. This phase can last for years.
During the latent stage, there are no symptoms, but blood tests can still detect the disease. It is important to note that the latent stage of syphilis can still transmit the infection to others if sexual contact occurs.