The hardest thing about working with complex numbers is understanding why you might want to. Before introducing complex numbers, let's backup and look at simpler examples of the need to deal with new numbers.
Whole numbers make sense.
You also learned about the operations of addition and subtraction, and you found that while subtraction is a perfectly good operation, some subtraction problems, like 3 - 5, don't have answers if we only work with whole numbers. Furthermore, by considering examples such as temperature scales, you see that negative numbers often make sense. Now we have fixed subtraction we will deal with division. Some, in fact most, division problems do not have answers that are integers. There is more to this story.