Unit 1: Number and Algebra
Topic 1.14: De Moivre & roots (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.14. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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If 5 − 2i is a root of a real-coefficient polynomial, another root is:
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A polynomial with real coefficients has root 4 − 3i. Write down another root and the real quadratic factor.
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Before using De Moivre on (2 + 2i)⁵ you must first:
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Find (2 cis(π/4))⁴, giving your answer in Cartesian form.
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The five fifth-roots of a complex number are spaced apart by:
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On an Argand diagram, the six sixth-roots of a number form a:
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Write down the angle between adjacent roots on the Argand diagram.
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Given z = 2 cis(π/12), find z⁶ in Cartesian form.
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Find the three cube roots of 27, in polar form.
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Find the fourth roots of 16, in polar form (−π < θ ≤ π).
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Explain why they lie on a circle, equally spaced.
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Given that 3i is a root of a quadratic with real coefficients, find the quadratic.
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