Further Maths De Moivre's theorem and roots of unity quiz to download as PDF

This Further Maths De Moivre's theorem and roots of unity quiz has 10 short questions for pupils aged 16-18. Type your answer, check it straight away and read the explanation when you get one wrong.

Further Maths De Moivre's theorem and roots of unity quiz: the 10 questions

Find \((\cos\tfrac\pi6+i\sin\tfrac\pi6)^{12}\).
What is \(|e^{i\theta}|\)?
How many cube roots does 8 have in \(\mathbb C\)?
\(e^{i\pi/2}=\)?
Find \((1-i)^2\).
Angle between consecutive 6th roots of unity (degrees)?
Sum of the 4th roots of unity?
Solve \(z^2=-1\).
If \(z=e^{i\pi/3}\), find \(z^3\).
Complete: \(\cos3\theta=4\cos^3\theta-\)?

How to use this Further Maths De Moivre's theorem and roots of unity quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the De Moivre's theorem and roots of unity lesson and try again later. After that, try the multiple choice questions or the De Moivre's theorem and roots of unity worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.