Roots of unity (HSC SSCE Mathematics Extension 2): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What are complex roots of unity?
What are complex roots of unity?
Solutions to z^n = 1
Where do roots of unity lie?
Where do roots of unity lie?
On the unit circle
What is the angle between roots?
What is the angle between roots?
360°/n
What does z^n - 1 factor into?
What does z^n - 1 factor into?
(z - 1)(z^{n-1} + ...)
What is ω in roots of unity?
What is ω in roots of unity?
e^{2πi/n}
How are roots of unity symmetrically placed?
How are roots of unity symmetrically placed?
Equal angular spacing
What is the result of ω^n?
What is the result of ω^n?
1
What pairs do roots of unity form?
What pairs do roots of unity form?
Conjugate pairs for even n
What is the significance of roots of unity?
What is the significance of roots of unity?
Polynomial factorisation
What does z^4 - 1 factor into?
What does z^4 - 1 factor into?
(z - 1)(z + 1)(z - i)(z + i)