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CXC CAPE · · Pure Mathematics

De Moivre's theorem and roots
Practice Questions

6 CXC CAPE Pure Mathematics questions on De Moivre's theorem and roots, each with instant feedback and a full examiner-style mark scheme.

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Try 2 sample questions on De Moivre's theorem and roots

Question 1 · 1 mark · Difficulty 3/3

De Moivre's theorem states (cos θ + i sin θ)ⁿ =

  1. n cos θ + i sin θ
  2. cos(θ/n) + i sin(θ/n)
  3. cos nθ + i sin nθ
  4. cos θ + i sin nθ
Show answer & explanation
✓ Answer: C — cos nθ + i sin nθ
De Moivre: raise to power n multiplies the angle by n.
Question 2 · 1 mark · Difficulty 3/3

A complex number written as r(cos θ + i sin θ) is in ____ form.

  1. exponential only
  2. polar (modulus-argument)
  3. Cartesian
  4. standard
Show answer & explanation
✓ Answer: B — polar (modulus-argument)
This is polar / modulus-argument form.
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20 questions · 25 min · free

CXC CAPE Pure Mathematics: De Moivre's theorem and roots FAQ

Is Kramizo free for CXC CAPE students preparing for Pure Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix De Moivre's theorem and roots practice with other Pure Mathematics topics or even switch to a totally different CXC CAPE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the De Moivre's theorem and roots questions aligned to the official CXC CAPE Pure Mathematics syllabus?
Every question is written against the published CXC CAPE Pure Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CXC CAPE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CXC CAPE.
How is De Moivre's theorem and roots typically tested on CXC CAPE Pure Mathematics papers?
De Moivre's theorem and roots appears across multiple question types on real CXC CAPE Pure Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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