Stage 31 · Complex Numbers

31.1.1 The Point You Can't Find on the Number Line

31.1 From Analytic Geometry to an Equation We Can't Solve

Point 1 of 4

31.1.1 The Point You Can't Find on the Number Line

Core idea

Picture this: x²=−1 has no answer anywhere on the number line, like asking "which length, when squared, comes out negative" — and that pushes us to invent a brand-new number i with the rule i²=−1

Module goal. Picking up the coordinate geometry from the last stage, we start from a genuine dead end — the real number line just isn't enough — and from there introduce the imaginary unit and the idea of complex numbers

eastmath.com · 31.1 From Analytic Geometry to an Equation We Can't Solve · 31.1.1 The Point You Can't Find on the Number Line