coming up with an idea
Conceiving is the process of arriving at an idea. If there were no artificial light in the world, one might conceive the need for some form of electric torch. That would be conceiving. But the design of an actual incandescent bulb versus a fluorescent one would require conceptualizing a specific implementation of the idea one has conceived. Conceiving need not come before conceptualizing. For example, a common dramatic technique is to give a character a very clear mental image of an object or arrangement that holds the solution to the story's problem. But the character does not know the solution lies in the conceptualization. It is only when he finally conceives of the need for a particular kind of solution that he realizes he had the answer all along. Simply put, Conceiving defines the question, Conceptualizing clarifies the answer.
syn. originating, inventing, devising, engendering, hatch ideas