Specialist Mathematics

Complex numbers, vectors, proof and calculus for Units 1 to 4, with every step shown.

Multiplying by i in the complex plane The point z = 3 + i is shown in blue. The point iz = −1 + 3i, drawn in orange, is z rotated 90 degrees anticlockwise about the origin, at the same distance from it. Re Im z iz
Multiplying \(z = 3 + i\) by \(i\) gives \(iz = -1 + 3i\): the same distance from the origin, turned through \(90^\circ\).
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Unit 3

Complex numbers

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Complex multiplication as rotation

Unit 3 · Complex numbers · Notes

Short notes and six questions on what multiplication does to points in the complex plane.

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Units 3–4

External exam

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Every past QCAA complex unfamiliar question, 2020–2025

Units 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.

Open: Every past QCAA complex unfamiliar question, 2020–2025

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