Which stage of the creative process is characterized as an unexpected moment when the idea comes, often when the mind is relaxed and doing something else?

The correct answer is illumination

Illumination refers to an "aha moment" when an unexpected creative idea suddenly comes into someone's mind while they are engaged in some type of activity unrelated to their creative problem at hand. Authors and creative artists such as painters and musicians often report experiencing moments of illumination, when they claim that an idea for a song suddenly popped into their mind, or an image of their next painting suddenly came into their mind.