Stage 31 · Complex Numbers

31.5.1 Trigonometric Form: Length Paired with Direction

31.5 The Trigonometric Form and Geometric Meaning of Complex Numbers

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31.5.1 Trigonometric Form: Length Paired with Direction

Core idea

Picture this: rather than report coordinates, report "how long the arrow is and which way it turns"; a+bi=r(cosθ+i sinθ), where r is the modulus and θ is the argument

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 · 31.5.1 Trigonometric Form: Length Paired with Direction