Stage 31 · Complex Numbers

31.5.2 What Multiplication Really Does: Add the Angles, Multiply the Lengths

31.5 The Trigonometric Form and Geometric Meaning of Complex Numbers

Point 2 of 4

31.5.2 What Multiplication Really Does: Add the Angles, Multiply the Lengths

Core idea

Picture this: multiply two complex numbers and the arrow lengths multiply while the arguments add — multiplying by a complex number is just one rotation plus one scaling

Module goal. We upgrade a complex number from a "coordinate address" to a "length plus direction," revealing that multiplication and division are really rotation and scaling — and laying groundwork for deeper material to come
eastmath.com · 31.5 The Trigonometric Form and Geometric Meaning of Complex Numbers · 31.5.2 What Multiplication Really Does: Add the Angles, Multiply the Lengths