For any real number x, x^2 must be ≥ 0. So an expression like x^2 = -1 has no real solutions.

Let’s imagine for a moment that x^2 = -1 does have a solution. It can’t be a real number, so we’ll have to suppose that there’s some imaginary number i such that i^2 = -1. What could we do with such a number i? What properties would it have?