De Moivre's theorem and roots of unity
Apply de Moivre's theorem; find nth roots of complex numbers and roots of unity
What you'll learn
- 1
Think of a Ferris wheel 🎡 with 4 equally spaced seats. Each seat is a 'root of unity' — a complex number that, when raised to a power, gives 1.
- 2
Here are the 4 fourth roots of unity on a circle. They're at 0°, 90°, 180°, and 270° around the unit circle. Each one, when raised to the 4th power, gives 1.
- 3
Let's find the 3 cube roots of unity using De Moivre's theorem.
- 4
Drag the points to place the 5 fifth roots of unity on the circle. They must be equally spaced!
- 5
How many degrees apart are the 6 sixth roots of unity?
- 6
Use the number line to find the 4th root of unity at angle 90°. What complex number is that?
- 7
According to De Moivre, what is (cos 30° + i sin 30°)⁶?
Practise De Moivre's theorem and roots of unity with Whizlo
Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.