ZIMSEC A-Level Pure Mathematics
6.7.2Polar form, equations, loci and de Moivre's theorem
Polar form, equations, loci and de Moivre's theorem in ZIMSEC A-Level Pure Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Subtopic57 practice questions3 lessons
Overview
Form 6. The polar form is taught with the Argand diagram in amaths.complex.argand-polar (6.7.1).
Learning objectives
What the syllabus expects you to be able to do.
- 6.7.2.1Form 6: solve polynomial equations (up to degree five) with at least one pair of non-real roots.
- 6.7.2.2Form 6: express complex numbers in polar form r(cos θ + i sin θ) = re^(iθ) and multiply and divide them in that form.
- 6.7.2.3Form 6: illustrate equations and inequalities involving complex numbers by loci in an Argand diagram.
- 6.7.2.4Form 6: derive and prove de Moivre's theorem and use it to prove trigonometrical identities and solve equations, including the nth roots of unity.
Lessons
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De Moivre's theorem and nth roots
45 min
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Loci in the Argand diagram
50 min
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Polynomial equations with complex roots
45 min
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Sample question
A sample question on this topic. Answer it, check it, then read the worked answer.
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