The answer is not that complex, complex numbers are as imaginary as negative numbers. And as we all know, negative numbers are quite useful to represent values that fluctuate a lot between two states, for example credit and debit.
So we can consider complex numbers to be the same. As a tool, it doesn't have a day-to-day application for a normal person, but they are incredibly important to solve complex mathematical problems which could have a direct impact on our life.