Complex Numbers (Preliminary Idea Only)

You already know how to count, measure, and even handle negative numbers and fractions. But what happens when you try to solve an equation like $x^2 + 1 = 0$? No real number squares to give $-1$, so we need a new kind of number. This is where the imaginary unit $i = \sqrt{-1}$ comes in, letting us build complex numbers of the form $a + ib$ — a simple but powerful …