I also teach precalculus, and I think it depends on the skill level of the students and how much time you have.

If it’s just something you want them to be able to work with and then move on from, it’s sufficient to treat the subject mechanically. But if you want something cool, here’s how I introduce it to my more advanced precalc class:

They already know the quadratic formula. In the renaissance, a cubic forumula was discovered. It’s intuitive that any cubic will have at least one real root, because the range is all real numbers. However, when you evaluate the cubic formula, sometimes you get a square root of -1 in an intermediate step. If you just keep working the problem through and don’t panic eventually it will cancel out, but you have to go through the complex plane to find your real root sometimes. This was the historical motivation for first working with imaginary numbers. It’s a very concrete, tangible way to introduce the subject. You can set up or find some mostly simplified cubics where they’ll have to intuitively start working with complex numbers. And the history is very colorful, including dueling mathematicians encoding the cubic formula in poetry, stealing formulas, etc.