De Moivre's theorem turns powers and roots of complex numbers into simple arithmetic on the modulus and argument, and generates trigonometric identities as a by-product.
Syllabus points covered
- Use de Moivre's theorem for positive and negative integer exponents
- Find the nth roots of a complex number and represent them on an Argand diagram
- Use complex numbers to derive trigonometric identities
- Use the exponential form re^(iθ) and sketch loci in the Argand diagram
Common mistakes
- Missing roots — there are always exactly n nth roots, spaced equally around a circle.
- Getting the argument in the wrong quadrant. Sketch the point before computing.
- Working in degrees when the exponential form requires radians.
- Forgetting to take the nth root of the modulus as well as dividing the argument.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
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