The first use of complex numbers was as intermediate quantities in the calculation of the roots of cubic polynomial functions. This use is analogous to using negative numbers in a ledger even though negative amounts of physical things don't make sense.

Edit: I meant physical things like apples fam. This is an important philosophical point we don't appreciate because we are so used to them. De Morgan once wrote:

"It is not our intention to follow the earlier algebraists through their different uses of negative numbers. These creations of algebra retained their existence, in the face of the obvious deficiency of rational explanation which characterized every attempt at their theory."