Complex multiplication as rotation
Unit 3 · Complex numbers · Notes
Short notes and six questions on what multiplication does to points in the complex plane.
Open: Complex multiplication as rotationComplex numbers, vectors, proof and calculus for Units 1 to 4, with every step shown.
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Unit 3 · Complex numbers · Notes
Short notes and six questions on what multiplication does to points in the complex plane.
Open: Complex multiplication as rotationUnits 3–4 · External exam · Interactive
All 24 Specialist complex unfamiliar questions from the 2020–2025 external exams, each with an animation and an interactive to work through, then the marking guide one mark at a time.
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Multiply a complex number by the imaginary unit and its point rotates a quarter-turn anticlockwise about the origin. Here is why, in three lines of algebra.