Exponential Form & de Moivre's Theorem (Edexcel A-Level Further Mathematics): Quizzes

📚Quizzes
Applications of de Moivre's Theorem
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

What does de Moivre's Theorem state for (cosθ+isin⁡θ)n(cos \theta + i \sin \theta)^n?

cos⁡(nθ)+isin⁡(nθ)\cos(n \theta) + i \sin(n \theta)

Using de Moivre's Theorem with n=2n=2, what is cos⁡(2θ)\cos(2\theta) equal to?

cos⁡2θ−sin⁡2θ\cos^2 \theta - \sin^2 \theta

Using de Moivre's Theorem with n=2n=2, what is sin⁡(2θ)\sin(2\theta) equal to?

2cos⁡θsin⁡θ2 \cos \theta \sin \theta

What are the solutions to (cos⁡θ+isin⁡θ)3=1(\cos \theta + i \sin \theta)^3 = 1 for θ\theta in [0,2π)[0, 2\pi)?

0,2π3,4π30, \frac{2\pi}{3}, \frac{4\pi}{3}

What are the 4th roots of 16?

2,2i,−2,−2i2, 2i, -2, -2i

What is cos⁡(3θ)\cos(3\theta) using the triple-angle formula?

cos⁡3θ−3cos⁡θsin⁡2θ\cos^3 \theta - 3 \cos \theta \sin^2 \theta

What is sin⁡(3θ)\sin(3\theta) using the triple-angle formula?

3cos⁡2θsin⁡θ−sin⁡3θ3 \cos^2 \theta \sin \theta - \sin^3 \theta

What is Euler's formula as used in summing trigonometric sequences?

eiθ=cos⁡θ+isin⁡θe^{i\theta} = \cos \theta + i \sin \theta

What type of series is 1+eiθ+ei2θ+⋯+einθ1 + e^{i\theta} + e^{i2\theta} + \dots + e^{in\theta}?

Geometric series

Which is NOT stated as an application of de Moivre's Theorem?

Finding derivatives of trig functions

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Explore Edexcel A-Level Further Mathematics Model Answers by Topics

Explore Edexcel A-Level Further Mathematics Flashcards by Topics

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

Join 100,000+ A-Level students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.