Cambridge AS & A Level Mathematics
3.9Complex numbers
Complex numbers in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Topic77 practice questions4 lessons
Learning objectives
What the syllabus expects you to be able to do.
- 3.9.1Paper 3: understand complex numbers, real and imaginary parts, modulus, argument and conjugate, and equality of complex numbers.
- 3.9.2Paper 3: add, subtract, multiply and divide complex numbers in Cartesian form.
- 3.9.3Paper 3: use the fact that non-real roots of a real polynomial occur in conjugate pairs.
- 3.9.4Paper 3: represent complex numbers on an Argand diagram.
- 3.9.5Paper 3: multiply and divide complex numbers in polar form r(cos θ + i sin θ) = re^(iθ).
- 3.9.6Paper 3: find the two square roots of a complex number.
- 3.9.7Paper 3: understand the geometric effects of conjugating, adding, subtracting, multiplying and dividing.
- 3.9.8Paper 3: illustrate simple equations and inequalities by loci in an Argand diagram.
Lessons
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Complex numbers in Cartesian form
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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The Argand diagram, modulus–argument and polar form
50 min
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Sample question
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