This turns out to be a useful way of thinking about alternating current, and you can analyse AC circuits using complex arithmetic in much the same way as you us

This turns out to be a useful way of thinking about alternating current, and you can analyse AC circuits using complex arithmetic in much the same way as you use real algebra to analyse DC circuits. "Userful way of thinking" and "analyse" something is not a real object strictly speaking - it is a process or phenomenon (no doubt complex numbers are useful here). But can you say what kind of real object or property a complex number represents or measures? For example, an integer can represent the number of apples and their weight is represented by a real number. What property of a real object can be expressed, for example, as 50i ?