Modulus and argument, complex quadratics, equations and square roots
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Two ways to say where a number is
- Modulus
Read the transcript of the teaching part
Last time
Before we start: last time, in Complex numbers, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Two ways to say where a number is
A point on a map can be given as east and north, or as a distance and a bearing. A complex number works the same way. Plus b i is the east and north version. The modulus and argument is the distance and bearing version. Switching between them, and then solving equations, is today's job.
Modulus
The modulus of a plus b i is the square root of a squared plus b squared. It is the length from the origin to the point. For 5 minus 12 i, the modulus is the square root of 25 plus 144, which is 13. The modulus is never negative, and the modulus of a product is the product of the moduli.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Modulus and argument · Solving complex equations · Square roots of a complex number.
The whole chapter: Complex Numbers.
Chapter 3.9: Complex numbers
- Complex numbers: arithmetic, roots, geometric effects and loci 6 min
- Modulus and argument, complex quadratics, equations and square roots 6 min
Also for A Level Maths 9709 Paper 3
Which topics come up most in A Level Maths 9709 Paper 3 past papers, counted from every paper since 2004.