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Complex numbers 2 — Question 19

QCAA 2025, Paper 1 · 6 marks

Q19 · 2025 · Technology-freeComplex unfamiliar6 marks

QUESTION 19 (6 marks)

Let w∈Cw\in\mathbb C be any fifth root of unity, where w∉Rw\notin\mathbb R. Show that w3(1+w)(1+w3)∈Z−.w^3(1+w)(1+w^3)\in\mathbb Z^-.
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