31.5.4 Multiplying by i Is a 90° Counterclockwise Turn
31.5 The Trigonometric Form and Geometric Meaning of Complex Numbers
Point 4 of 4
31.5.4 Multiplying by i Is a 90° Counterclockwise Turn
Core idea
Picture this: i has modulus 1 and argument 90°, so multiplying by it leaves the arrow's length alone and just turns it a right angle — the simplest algebraic switch for rotation
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 · 31.5.4 Multiplying by i Is a 90° Counterclockwise Turn